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Exam Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) The table below shows the number of new AIDS cases in the U.S. in each of the years 1989-1994. 1) Year New AIDS cases 1989 33,643 1990 41,761 1991 43,771 1992 45,961 1993 103,463 1994 61,301 Classify the study as either descriptive or inferential. A) Descriptive B) Inferential 2) Based on a random sample of 1000 people, a researcher obtained the following estimates of the percentage of people lacking health insurance in one U.S. city. 2) Age Percentage not covered 18-24 28.2 25-39 24.9 40-54 19.1 55-65 16.5 Classify the study as either descriptive or inferential. A) Descriptive B) Inferential 3) A researcher randomly selects a sample of 100 students from the students enrolled at a particular college. She asks each student his age and calculates the mean age of the 100 students. It is 21.3 years. Based on this sample, she then estimates the mean age of all students enrolled at the college to be 21.3 years. In what way are descriptive statistics involved in this example? In what way are inferential statistics involved? A) When calculating the mean age of the students in the sample, the researcher is using inferential statistics. When estimating the mean age of all students at the college, the researcher is using descriptive statistics. B) When calculating the mean age of the students in the sample, the researcher is using descriptive statistics. When estimating the mean age of all students at the college, the researcher is using inferential statistics. 1 3) 4) A news article appearing in a national paper stated that ʺThe fatality rate from use of firearms sank to a record low last year, the government estimated Friday. But the overall number of violent fatalities increased slightly, leading the government to urge an increase in police forces in major urban areas. Overall, 15,600 people died from violent crimes in 2005, up from 15,562 in 2004, according to projections from a government source. Is the figure15,600 a descriptive statistic or an inferential statistic? Is the figure 15,562 a descriptive statistic or an inferential statistic? A) The figure15,600 is a descriptive statistic since it reflects the actual number of deaths from violent crimes for the year 2004. The figure15,562 is an inferential statistic since it is indicated in the statement that it is a projection (probably based on incomplete data for the year 2005). B) The figure15,600 is an inferential statistic since it is indicated in the statement that it is a projection (probably based on incomplete data for the year 2004). The figure15,562 is an inferential statistic as well. C) The figure15,600 is a descriptive statistic since it reflects the actual number of deaths from violent crimes for the year 2005. The figure15,562 is a descriptive statistic as well. D) The figure15,600 is an inferential statistic since it is indicated in the statement that it is a projection (probably based on incomplete data for the year 2005). The figure 15,562 is a descriptive statistic since it reflects the actual number of deaths from violent crimes for the year 2004. Answer the question. 5) 100,000 randomly selected adults were asked whether they drink at least 48 oz of water each day and only 45% said yes. Identify the sample and population. A) Sample: the 100,000 selected adults; population: the 45% of adults who drink at least 48 oz of water B) Sample: the 45% of adults who drink at least 48 oz of water; population: all adults C) Sample: the 100,000 selected adults; population: all adults D) Sample: all adults ; population: the 100,000 selected adults Identify the study as an observational study or a designed experiment. 6) 400 patients suffering from chronic back pain were randomly assigned to one of two groups. Over a four-month period, the first group received acupuncture treatments and the second group received a placebo. Patients who received acupuncture treatments improved more than those who received the placebo. A) Designed experiment B) Observational study 7) An examination of the medical records of 10, 000 women showed that those who were short and fair skinned had a higher risk of osteoperosis. A) Designed experiment B) Observational study SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 8) Why do statisticians sometimes use inferential statistics to draw conclusions about a population? In what situations might a statistician draw conclusions about a population using descriptive statistics only? 2 8) 4) 5) 6) 7) 9) At one hospital in 1992, 674 women were diagnosed with breast cancer. Five years later, 88% of the Caucasian women and 63% of the African American women were still alive. This observational study shows an association between race and breast cancer survival--that Caucasian women are more likely to survive breast cancer than African American women. How could this study be modified to make it a designed experiment? Comment on the feasibility of the designed experiment that you described. 9) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. List all possible samples from the specified population. 10) Given a group of students: Allen (A), Brenda (B), Chad (C), Dorothy (D), and Eric (E), list all of the possible samples (without replacement) of size four that can be obtained from the group. A) A,B,C,D A,B,C,E A,C,D,E A,D,E,B B,C,D,E B,C,E,A B,D,E,A C,A,B,D C,E,D,B D,A,C,E B) A,B,C,D A,B,C,E A,C,D,E A,D,E,B B,C,D,E C) A,B,C,D D) A,B,C,D A,B,C,E A,C,D,E A,D,E,B Provide an appropriate response. 11) The finalists in an essay competition are Lisa (L), Melina (M), Ben (B), Danny (D), Eric (E), and Joan (J). Consider these finalists to be a population of interest. The possible samples (without replacement) of size two that can be obtained from this population of six finalists are as follows. 10) 11) L,M L,B L,D L,E L,J M,B M,D M,E M,J B,D B,E B,J D,E D,J E,J If a simple random sampling method is used to obtain a sample of two of the finalists, what are the chances of selecting Lisa and Danny? 1 1 1 2 B) C) D) A) 6 3 15 15 12) From a group of 496 students, every 49th student starting with the 3rd student is selected. Identify the type of sampling used in this example. A) Simple random sampling B) Cluster sampling C) Systematic random sampling D) Stratified sampling 12) 13) An education researcher randomly selects 38 schools from one school district and interviews all the teachers at each of the 38 schools. Identify the type of sampling used in this example. A) Stratified sampling B) Cluster sampling C) Simple random sampling D) Systematic random sampling 13) 14) At a college there are 120 freshmen, 90 sophomores, 110 juniors, and 80 seniors. A school administrator selects a simple random sample of 12 of the freshmen, a simple random sample of 9 of the sophomores, a simple random sample of 11 of the juniors, and a simple random sample of 8 of the seniors. She then interviews all the students selected. Identify the type of sampling used in this example. A) Cluster sampling B) Systematic random sampling C) Simple random sampling D) Stratified sampling 14) 3 15) A pollster uses a computer to generate 500 random numbers and then interviews the voters corresponding to those numbers. Identify the type of sampling used in this example. A) Stratified sampling B) Systematic random sampling C) Cluster sampling D) Simple random sampling A designed experiment is described. Identify the specified element of the experiment. 16) In a clinical trial, 780 participants suffering from high blood pressure were randomly assigned to one of three groups. Over a one-month period, the first group received a low dosage of an experimental drug, the second group received a high dosage of the drug, and the third group received a placebo. The diastolic blood pressure of each participant was measured at the beginning and at the end of the period and the change in blood pressure was recorded. Identify the experimental units (subjects). A) The participants in the experiment B) The three different groups C) The treatment (i.e., placebo, low dosage of drug, or high dosage of drug) D) The diastolic blood pressures of the participants 15) 16) 17) In a clinical trial, 780 participants suffering from high blood pressure were randomly assigned to one of three groups. Over a one-month period, the first group received a low dosage of an experimental drug, the second group received a high dosage of the drug, and the third group received a placebo. The diastolic blood pressure of each participant was measured at the beginning and at the end of the period and the change in blood pressure was recorded. Identify the response variable. A) The treatment received (placebo, low dosage, high dosage) B) The dosage of the drug C) Change in diastolic blood pressure D) The participants in the experiment 17) 18) In a clinical trial, 780 participants suffering from high blood pressure were randomly assigned to one of three groups. Over a one-month period, the first group received a low dosage of an experimental drug, the second group received a high dosage of the drug, and the third group received a placebo. The diastolic blood pressure of each participant was measured at the beginning and at the end of the period and the change in blood pressure was recorded. Identify the factor. A) Diastolic blood pressure B) The experimental drug C) The participants in the experiment D) The dosage of the drug 18) 19) In a clinical trial, 780 participants suffering from high blood pressure were randomly assigned to one of three groups. Over a one-month period, the first group received a low dosage of an experimental drug, the second group received a high dosage of the drug, and the third group received a placebo. The diastolic blood pressure of each participant was measured at the beginning and at the end of the period and the change in blood pressure was recorded. Identify the levels of the factor. A) Diastolic blood pressure at the start, diastolic blood pressure at the end B) Placebo, low dosage, high dosage C) High blood pressure, low blood pressure D) The experimental drug 19) 4 20) In a clinical trial, 780 participants suffering from high blood pressure were randomly assigned to one of three groups. Over a one-month period, the first group received a low dosage of an experimental drug, the second group received a high dosage of the experimental drug, and the third group received a placebo. The diastolic blood pressure of each participant was measured at the beginning and at the end of the period and the change in blood pressure was recorded. Identify the treatments. A) Placebo, low dosage of drug, high dosage of drug B) Low dosage of drug, high dosage of drug C) Diastolic blood pressure at start, diastolic blood pressure at end D) The experimental drug 20) 21) A herpetologist performed a study on the effects of the body type and mating call of the male bullfrog as signals of quality to mates. Four life-sized dummies of male bullfrogs and two sound recordings provided a tool for testing female response to the unfamiliar frogs whose bodies varied by size (large or small) and color (dark or light) and whose mating calls varied by pitch (high, normal, or low). The female bullfrogs were observed to see whether they approached each of the four life-sized dummies. Identify the treatments. A) The eight different possible combinations of the two body sizes, two body colors, and two mating call pitches B) The twelve different possible combinations of the three body sizes, two body colors, and two mating call pitches C) The eighteen different possible combinations of the two body sizes, three body colors, and three mating call pitches D) The twelve different possible combinations of the two body sizes, two body colors, and three mating call pitches 21) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 22) Explain the difference between an observational study and a designed experiment. 22) 23) In a designed experiment, explain the difference between the treatments and the factors. 23) 24) A study was conducted to evaluate the effectiveness of a new diet pill for men. A group of 3000 men were involved in the study. Of these 3000 men, 2311 took the diet pill and 889 were given a placebo. Identify the treatments, the treatment group, and the control group. 24) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Classify the data as either qualitative or quantitative. 25) The following table gives the top five movies at the box office this week. Rank 1 2 3 4 5 Last week N/A 2 1 5 4 Movie title Pirate Adventure Secret Agent Files Epic Super Hero Team Reptile Ride Must Love Cats Studio Movie Giant G.M.G. 21st Century Movie Giant Dreamboat Box office sales ($ millions) 35.2 19.5 14.3 10.1 9.9 What kind of data is provided by the information in the second column? A) Qualitative B) Quantitative 5 25) 26) The following table gives the top five movies at the box office this week. Rank 1 2 3 4 5 Last week N/A 2 1 5 4 Movie title Pirate Adventure Secret Agent Files Epic Super Hero Team Reptile Ride Must Love Cats Studio Movie Giant G.M.G. 21st Century Movie Giant Dreamboat 26) Box office sales ($ millions) 35.2 19.5 14.3 10.1 9.9 What kind of data is provided by the information in the third column? A) Qualitative B) Quantitative Classify the data as either discrete or continuous. 27) The number of freshmen entering college in a certain year is 621. A) Discrete B) Continuous 28) The average height of all freshmen entering college in a certain year is 68.4 inches. A) Discrete B) Continuous Identify the variable. 29) The following table shows the average weight of offensive linemen for each given football team. Team Gators Lakers Eagles Pioneers Lions Mustangs Rams Buffalos 27) 28) 29) Average weight (pounds) 303.52 326.78 290.61 321.96 297.35 302.49 345.88 329.24 Identify the variable under consideration in the second column? A) pounds B) Gators C) team name D) average weight of offensive linemen Tell whether the statement is true or false. 30) A discrete variable always yields numerical values. A) True 30) B) False 31) The possible values of a discrete variable always form a finite set. A) True B) False 31) 32) A variable whose values are observed by counting something must be a discrete variable. A) True B) False 32) 33) The set of possible values that a variable can take constitutes the data. A) True B) False 33) 6 34) A discrete variable can only yield whole-number values. A) True B) False 34) 35) A variable whose possible values are 1.15, 1.20, 1.25, 1.30, 1.35, 1.40, 1.45, 1.50, 1.55, 1.60, is a continuous variable. A) True B) False 35) 36) A variable which can take any real-number value in the interval [ 0, 1 ] is a continuous variable. A) True B) False 36) 37) A personʹs blood type can be classified as A, B, AB, or O. In this example, ʺblood typeʺ is the variable while A, B, AB, O constitute the data. A) True B) False 37) 38) Arranging the age of students in a class in from youngest to oldest yields ordinal data. A) True B) False 38) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Construct a grouped-data table for the given data. Use the symbol to mean ʺup to, but not includingʺ. 39) A medical research team studied the ages of patients who had strokes caused by stress. 39) The ages of 34 patients who suffered stress strokes were as follows. 29 30 36 41 45 50 57 61 28 50 36 58 60 38 36 47 40 32 58 46 61 40 55 32 61 56 45 46 62 36 38 40 50 27 Construct a frequency table for these ages. Use 8 classes beginning with a lower class limit of 25. Age Frequency 7 40) A government researcher was interested in the starting salaries of humanities graduates. A random sample of 30 humanities graduates yielded the following annual salaries. Data are in thousands of dollars, rounded to the nearest hundred dollars. 40) 23.1 24.0 33.7 28.4 36.0 41.0 22.2 21.8 30.5 49.2 30.1 25.2 38.3 46.1 40.0 27.5 24.9 28.0 31.8 29.9 25.7 32.5 48.6 27.4 41.4 35.9 31.9 42.4 26.3 33.0 Construct a grouped-data table for these annual starting salaries. Use 20 as the first cutpoint and classes of equal width 4. Salary Frequency Construct a grouped-data table for the given data. Use the alternate method for depicting classes. Using this method, the range of values that go into a given class includes both cutpoints. So the class 30 -39, for example, would contain values from 30 up to and including 39. 41) 41) A medical research team studied the ages of patients who had strokes caused by stress. The ages of 34 patients who suffered stress strokes were as follows. 29 30 36 41 45 50 57 61 28 50 36 58 60 38 36 47 40 32 58 46 61 40 55 32 61 56 45 46 62 36 38 40 50 27 Construct a frequency table for these ages. Use 8 classes beginning with a lower class limit of 25. Age Frequency 8 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Construct a frequency distribution for the given qualitative data. 42) The blood types for 40 people who agreed to participate in a medical study were as follows. O A A O A O B A A A O O O B A O O O A A AB O O O O O B O B A AB A B O O A O A O AB Construct a frequency distribution for the data. A) Blood type Frequency O A B AB C) Blood type O A B AB 42) 19 13 5 3 Frequency B) Blood type Frequency O A B AB D) Blood type 19 11 5 2 Frequency 18 14 5 3 O A B AB 20 13 4 3 Provide the requested table entry. 43) The data in the following table show the results of a survey of college students asking which vacation destination they would choose given the eight choices shown. Determine the value that should be entered in the relative frequency column for Puerto Rico. Destination Frequency Relative frequency Florida 26 Mexico 78 Belize 13 Puerto Rico 28 Alaska 2 California 21 Colorado 18 Arizona 14 A) 28 B) 0.14 C) 0.014 9 D) 0.28 43) 44) The data in the following table reflect the amount of time 40 students in a section of Statistics 101 spend on homework each day. Find the value of the missing entry. 44) Homework time Relative (minutes) frequency 0-14 0.05 15-29 0.10 30-44 0.25 45-59 60-74 0.15 75-89 0.05 A) 40% B) 0.40 C) 16 D) The value cannot be determined from the given data. 45) The data in the following table represent heights of students at a highschool. Find the value of the missing entry. Height Relative (centimeters) frequency 0.03 142 152 152 162 0.21 0.27 162 172 172 182 0.28 182 192 192 202 0.02 A) 0.21 B) 19% C) 0.19 D) The value cannot be determined from the given data. SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 46) When constructing a grouped-data table, what is the disadvantage of having too many classes? What is the disadvantage of having too few classes? 47) Anna set up a grouped-data table with the following classes: Number of sick days taken Frequency 0-3 3-6 6-9 9-12 What is wrong with these classes? Describe two ways the classes could have been correctly depicted. 10 46) 47) 45) 48) Suppose you are comparing frequency data for two different groups, 25 managers and 150 blue collar workers. Why would a relative frequency distribution be better than a frequency distribution? Construct the specified histogram. 49) The frequency table below shows the number of days off in a given year for 30 police detectives. Days off Frequency 10 0 2 2 4 1 7 4 6 6 8 7 1 8 10 10 12 4 Construct a frequency histogram. 11 48) 49) Construct the requested histogram. 50) The table gives the frequency distribution for the data involving the number of radios per household for a sample of 80 U.S. households. # of Radios 1 2 3 4 5 50) Frequency 5 10 30 25 10 Construct a relative frequency histogram. 0.625 0.5 0.375 0.25 0.125 1 2 3 4 5 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Construct a dotplot for the given data. 51) Attendance records at a school show the number of days each student was absent during the year. The days absent for each student were as follows. 9 3 4 2 8 6 3 4 0 6 7 3 4 2 2 A) B) C) D) 12 51) Construct a stem-and-leaf diagram for the given data. 52) The diastolic blood pressures for a sample of patients at a clinic were as follows. The measurements are in mmHg. 78 94 79 88 87 85 81 95 91 81 96 78 85 95 88 74 97 102 77 106 100 85 105 85 52) 73 90 110 105 84 111 83 92 89 101 83 120 87 92 114 83 B) A) 7 8 9 10 11 12 7 8 3 7 9 8 4 8 7 5 5 1 4 3 1 8 5 9 3 8 5 7 3 9 1 7 0 4 5 2 6 5 2 10 2 0 5 6 1 0 1 5 4 8 3 7 9 8 4 7 5 5 1 4 3 1 8 5 9 3 8 5 7 3 1 7 0 4 5 2 6 5 2 2 5 6 0 1 5 0 1 4 0 Construct a pie chart representing the given data set. 53) The following figures give the distribution of land (in acres) for a county containing 88,000 acres. Land Use Acres Relative Frequency Forest 13,200 0.15 Farm 8800 0.10 Urban 66,000 0.75 A) B) Construct the requested graph. 13 53) 54) Construct a bar graph for the relative frequencies given. Blood type O A B AB Frequency 22 19 6 3 Relative frequency 0.44 0.38 0.12 0.06 A) B) C) 14 54) A nurse measured the blood pressure of each person who visited her clinic. Following is a relative -frequency histogram for the systolic blood pressure readings for those people aged between 25 and 40. Use the histogram to answer the question. The blood pressure readings were given to the nearest whole number. 55) Approximately what percentage of the people aged 25-40 had a systolic blood pressure reading between 110 and 119 inclusive? A) 0.35% B) 35% C) 3.5% D) 30% 55) 56) Approximately what percentage of the people aged 25-40 had a systolic blood pressure reading between 110 and 139 inclusive? A) 74% B) 89% C) 59% D) 39% 56) 57) Approximately what percentage of the people aged 25-40 had a systolic blood pressure reading greater than or equal to 130? A) 26% B) 74% C) 23% D) 15% 57) 58) Approximately what percentage of the people aged 25-40 had a systolic blood pressure reading less than 120? A) 3.5% B) 50% C) 35% D) 5% 58) 59) Given that 300 people were aged between 25 and 40, approximately how many had a systolic blood pressure reading between 140 and 149 inclusive? A) 240 B) 2 C) 24 D) 8 59) 60) Given that 400 people were aged between 25 and 40, approximately how many had a systolic blood pressure reading of 140 or higher? A) 11 B) 32 C) 44 D) 8 60) 61) Given that 200 people were aged between 25 and 40, approximately how many had a systolic blood pressure reading between 130 and 149 inclusive? A) 5 B) 30 C) 46 D) 23 61) 62) Given that 200 people were aged between 25 and 40, approximately how many had a systolic blood pressure reading less than 130? A) 15 B) 48 C) 148 D) 74 62) 15 63) Identify the midpoint of the third class. A) 120 B) 130 63) C) 125 64) What common class width was used to construct the frequency distribution? A) 11 B) 10 C) 100 D) 124 64) D) 9 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Construct a relative-frequency polygon for the given data. 65) The table contains the frequency and relative-frequency distributions for the ages of the employees in a particular company department. 65) Age (years) Frequency Relative frequency 3 0.1875 20 30 6 0.375 30 40 40 50 4 0.25 1 0.0625 50 60 60 70 2 0.125 0.375 Relative frequency 0.25 0.125 20 25 30 35 40 45 50 55 60 65 70 Age (years) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide the requested response. 66) The table contains data from a study of daily study time for 40 students from Statistics 101. Construct an ogive from the data. Minutes on Number of Relative Cumulative homework students frequency relative frequency 2 0.05 0.05 0 15 4 0.10 0.15 15 30 30 45 8 0.20 0.35 18 0.45 0.80 45 60 60 75 4 0.10 0.90 4 0.10 1.00 75 90 16 66) A) B) C) D) The table does not contain enough information to construct an ogive. 17 A graphical display of a data set is given. Identify the overall shape of the distribution as (roughly) bell -shaped, triangular, uniform, reverse J-shaped, J-shaped, right skewed, left skewed, bimodal, or multimodal. 67) 67) A relative frequency histogram for the sale prices of homes sold in one city during 2006 is shown below. B) Reverse J-shaped D) Right skewed A) J-shaped C) Left skewed 68) A relative frequency histogram for the heights of a sample of adult women is shown below. A) J-shaped B) Triangular C) Bell-shaped 18 D) Left skewed 68) 69) A die was rolled 200 times and a record was kept of the numbers obtained. The results are shown in the relative frequency histogram below. A) Left skewed C) Triangular B) J-shaped D) Uniform 70) Two dice were rolled and the sum of the two numbers was recorded. This procedure was repeated 400 times. The results are shown in the relative frequency histogram below. A) Triangular B) Right-skewed C) Bell-shaped B) Reverse J-shaped D) Right skewed 19 70) D) Left skewed 71) The ages of a group of patients being treated at one hospital for osteoporosis are summarized in the frequency histogram below. A) Bell-shaped C) Left skewed 69) 71) 72) A frequency histogram is given below for the weights of a sample of college students. A) Multimodal B) Uniform C) Bell-shaped 72) D) Bimodal A graphical display of a data set is given. State whether the distribution is (roughly) symmetric, right skewed, or left skewed. 73) 73) A relative frequency histogram for the sale prices of homes sold in one city during 2006 is shown below. A) Left skewed B) Symmetric C) Right skewed 20 74) A relative frequency histogram for the heights of a sample of adult women is shown below. A) Symmetric B) Right skewed C) Left skewed 75) A die was rolled 200 times and a record was kept of the numbers obtained. The results are shown in the relative frequency histogram below. A) Symmetric B) Right skewed B) Symmetric C) Left skewed 21 75) C) Left skewed 76) Two dice were rolled and the sum of the two numbers was recorded. This procedure was repeated 400 times. The results are shown in the relative frequency histogram below. A) Right skewed 74) 76) 77) The ages of a group of patients being treated at one hospital for osteoporosis are summarized in the frequency histogram below. A) Symmetric B) Left skewed C) Right skewed 78) 78) A frequency histogram is given below for the weights of a sample of college students. A) Left skewed 77) B) Symmetric C) Right skewed SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 79) Hospital records show the age at death of patients who die while in the hospital. A frequency histogram is constructed for the age at death of the people who have died at the hospital in the past five years. Roughly what shape would you expect for the distribution? Why? 79) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the mean for the given sample data. Unless otherwise specified, round your answer to one more decimal place than that used for the observations. 80) Last year, nine employees of an electronics company retired. Their ages at retirement are listed 80) below. Find the mean retirement age. 50 62 61 52 62 58 65 52 55 A) 57.4 yr B) 58.0 yr C) 56.2 yr 22 D) 56.8 yr Solve the problem. If necessary, round your answer to one more decimal place than that used for the observations. 81) 81) A sample of non-recyclable waste shipping companies in a certain state yielded the following amounts, in tons, of waste shipped during 2005. Determine n, ∑xi , and x. 1192 419 849 1101 453 654 A) n = 12; ∑xi = 10,104; 878 512 791 x = 918.5 739 1673 843 B) n = 12; ∑xi = 10,104; C) n = 11; ∑xi = 10,104; x = 842 x = 842 D) n = 11; ∑xi = 10,104; x = 918.5 82) A scientist used the following data set showing the weight in pounds gained (or lost) by a sample of eight laboratory animals given Drug X. Determine n, ∑xi , and x. 8.0 -7.3 2.4 -2.4 A) n = 10; ∑xi = 5.6; x = 0.56 2.5 5.0 3.0 -5.6 B) n = 8; ∑xi = 5.6; C) n = 8; ∑xi = 5.6; D) n = 10; ∑xi = 5.6; x = 0.56 x = 0.7 x = 0.7 Find the median for the given sample data. 83) The salaries of ten randomly selected doctors are shown below. 82) 83) $150,000 $143,000 $165,000 $238,000 $215,000 $129,000 $139,000 $723,000 $217,000 $166,000 A) $165,500 B) $165,000 C) $229,000 D) $254,000 Find the mode(s) for the given sample data. 84) The blood types for 30 people who agreed to participate in a medical study were as follows. 84) O A A O A AB O B A O A O A B O O O AB A A A B O A A O O B O O Find the mode of the blood types. A) O B) 13 C) O, A D) A 85) Last year, nine employees of an electronics company retired. Their ages at retirement are listed below. Find the mode(s). 52 59 60 55 51 62 67 58 50 A) 52, 59, 60, 55, 51, 62, 67, 58, 50 C) No mode B) 57.1 D) 58 23 85) Find the range for the given data. 86) The weights, in pounds, of 18 randomly selected adults are given below. 86) 120 165 187 143 119 132 127 156 179 159 180 202 114 146 151 168 173 144 A) 78 lb B) (114, 202) lb C) 202 lb D) (120, 202) lb E) 88 lb Find the sample standard deviation for the given data. Round your final answer to one more decimal place than that used for the observations. 87) 15, 42, 53, 7, 9, 12, 14, 28, 47 87) A) 29.1 B) 16.6 C) 17.8 D) 15.8 Find the range and standard deviation for each of the two samples, then compare the two sets of results. 88) When investigating times required for drive-through service, the following results (in seconds) were obtained. Restaurant A 120 123 153 128 124 118 154 110 Restaurant B 115 126 147 156 118 110 145 137 A) Restaurant A: 46; 16.9 Restaurant B: 44; 16.2 Both measures indicate there is more variation in the data for restaurant A than the data for restaurant B. B) Restaurant A: 44; 16.1 Restaurant B: 46; 16.9 Both measures indicate there is more variation in the data for restaurant B than the data for restaurant A. C) Restaurant A: 44; 16.2 Restaurant B: 46; 16.9 Both measures indicate there is more variation in the data for restaurant B than the data for restaurant A. D) Restaurant A: 46; 16.2 Restaurant B: 44; 16.9 It is inconclusive as to which data set has more variation. 24 88) Provide an appropriate response. 89) The manager of a bank recorded the amount of time each customer spent waiting in line during peak business hours one Monday. The frequency distribution below summarizes the results. Find the standard deviation. Round your answer to one decimal place. Waiting time Number of (minutes) customer 14 0 4 4 8 11 7 8 12 12 16 16 0 16 20 20 24 2 A) 5.6 B) 5.3 C) 7.0 D) 5.9 90) A companyʹs raw-data sample of weekly salaries (in dollars) is shown below. 230 340 320 590 780 980 600 350 500 450 460 290 470 400 490 580 570 890 680 410 860 540 530 690 A frequency distribution of this data set is presented below, with a third column showing the class midpoints. Salary 200 300 400 500 600 700 800 900 300 400 500 600 700 800 900 1000 Frequency f 2 3 6 6 3 1 2 1 Midpoint x 250 350 450 550 650 750 850 950 (i) Use the raw data to obtain the sample standard deviation of the ungrouped data. Round your answer to two decimal places. (ii) Use the grouped-data formula to obtain the sample standard deviation of the grouped data in the frequency distribution. Round your answer to two decimal places. (iii) Compare your answers in parts (i) and (ii). A) (i) The sample standard deviation of the ungrouped data is 194.48; (ii) The sample standard deviation of the grouped data is 194.48; (iii) The results in parts (i) and (ii) are the same. The grouped data formula will always provide the actual standard deviation when the data are grouped in classes each based on a single value because the class midpoint is the same as each observation in each class. B) (i) The sample standard deviation of the ungrouped data is 195.32; (ii) The sample standard deviation of the grouped data is 171.84; (iii) The results in parts (i) and (ii) are different. This discrepancy occurs because in the grouped data formulas, every actual data value in a given class is replaced by the class midpoint even though most values in the class are not equal to the midpoint. 25 89) 90) C) (i) The sample standard deviation of the ungrouped data is 171.84; (ii) The sample standard deviation of the grouped data is 171.84; (iii) The results in parts (i) and (ii) are the same. The grouped data formula will always provide the actual standard deviation when the data are grouped in classes each based on a single value because the class midpoint is the same as each observation in each class. D) (i) The sample standard deviation of the ungrouped data is 194.48; (ii) The sample standard deviation of the grouped data is 182.52; (iii) The results in parts (i) and (ii) are different. This discrepancy occurs because in the grouped data formulas, every actual data value in a given class is replaced by the class midpoint even though most values in the class are not equal to the midpoint. Determine the quartile or interquartile range as specified. 91) The weights (in pounds) of 17 randomly selected adults are given below. Find the interquartile range. 144 165 187 143 119 132 127 156 179 159 180 202 114 146 151 168 173 A) 37 lb B) 30 lb C) 37.5 lb D) 38 lb 92) The weights (in pounds) of 18 randomly selected adults are given below. Find the third quartile, Q . 3 120 165 187 143 119 132 127 156 179 159 180 202 114 146 151 168 173 144 A) 170.5 lb B) 173 lb C) 176 lb The number of years of teaching experience is given below for 12 high -school teachers. 28 13 12 22 93) B) 5.1, 14.00, 21.95, 33.30, 51.7 inches D) 5.1, 13.300, 21.95, 31.175, 51.7 inches Provide an appropriate response. 94) Obtain the population standard deviation, σ, for the given data. Assume that the data represent population data. Round your final answer to one more decimal place than that used for the observations. 26 27 28 17 8 5 A) 69.1 yr 92) D) 174.5 lb Obtain the five-number summary for the given data. 93) The normal annual precipitation (in inches) is given below for 21 different U.S. cities. 39.1 32.3 18.5 35.4 27.1 27.8 8.6 23.5 42.6 34.3 21.5 12.0 5.1 12.6 22.4 10.9 16.4 25.4 17.2 15.4 51.7 A) 5.1, 13.300, 22.4, 31.175, 51.7 inches C) 5.1, 15.4, 22.4, 32.3, 51.7 inches 91) 19 31 B) 10.5 yr C) 8.3 yr 26 D) 8.7 yr 94) 95) Following is the number of reported cases of influenza for two cities for the years 1996 through 2005: 95) City A 1163 1954 1487 1864 1779 1244 1332 1299 1353 1802 City B 937 1023 843 829 965 1011 943 831 976 858 (i) Without doing any calculations, decide for which city the standard deviation of the number cases of influenza is larger. Explain. (ii) Find the individual population standard deviations of the number of cases of influenza. Round your final answer to two decimal places. Compare these answers with part (i). A) (i) The range of the values for City A is 791, while it is only 192 for City B, so City A is likely to have the larger standard deviation. (ii) City Aʹs population standard deviation is 277.40; City Bʹs population standard deviation is 71.29, so City A did have the larger standard deviation. B) (i) The range of the values for City A is 767, while it is only 121 for City B, so City A is likely to have the larger standard deviation. (ii) City Aʹs population standard deviation is 277.37; City Bʹs population standard deviation is 72.01, so City A did have the larger standard deviation. C) (i) The range of the values for City A is 791, while it is only 192 for City B, so City A is likely to have the larger standard deviation. (ii) City Aʹs population standard deviation is 278.43; City Bʹs population standard deviation is 71.25, so City A did have the larger standard deviation. D) (i) The range of the values for City A is 767, while it is only 121 for City B, so City A is likely to have the larger standard deviation. (ii) City Aʹs population standard deviation is 261.80; City Bʹs population standard deviation is 69.47, so City A did have the larger standard deviation. Solve the problem. 96) Scores on a test have a mean of 72 and a standard deviation of 9. Michelle has a score of 81. Convert Michelleʹs score to a z-score. A) -9 B) -1 C) 1 D) 9 96) 97) The mean of a set of data is 4.19 and its standard deviation is 2.77. Find the z-score for a value of 12.32. Round your final answer to two decimal places. A) 3.23 B) 3.24 C) 2.65 D) 2.94 97) 98) The mean of a set of data is -3.89 and its standard deviation is 3.83. Find the z-score for a value of 5.58. Round your final answer to two decimal places. A) 2.47 B) 2.77 C) 2.22 D) 2.72 98) 99) The mean of a set of data is 132.41 and its standard deviation is 71.48. Find the z-score for a value of 319.06. Round your final answer to two decimal places. A) 2.91 B) 2.61 C) 2.87 D) 2.35 99) 100) A variable x has a mean, μ, of 21.4 and a standard deviation, σ, of 5.1. Determine the z-score corresponding to an observed value for x of 20.4. Round your final answer to two decimal places. A) -0.20 B) 8.20 C) 0.20 D) 0.71 27 100) 101) A meteorological office keeps records of the annual precipitation in different cities. For one city, the mean annual precipitation is 31.5 and the standard deviation of the annual precipitation amounts is 3.8. Let x represent the annual precipitation in that city. Determine the z -score for an annual precipitation in that city of 23.5 inches. Round your final answer to two decimal places. A) 2.11 B) 14.47 C) 0.63 D) -2.11 101) 102) A variable x has a mean, μ, of 10 and a standard deviation, σ, of 7. Determine the standardized version of x. x - 10 10 x - 7 z - 10 B) z = C) z = D) z = A) x = 7 7 10 7 102) 103) A meteorological office keeps records of the annual precipitation in different cities. For one city, the mean annual precipitation is 15.3 and the standard deviation of the annual precipitation amounts is 4.2. Let x represent the annual precipitation in that city. Determine the standardized version of x. x - 4.2 z - 15.3 x - 15.3 15.3 B) z = C) z = D) x = A) z = 15.3 4.2 4.2 4.2 103) 104) A variable x has the possible observations shown below. 104) Possible observations of x: -3 -1 0 1 1 2 4 4 5 Determine the standardized version of x. Round the values of μ and σ to one decimal place. A) z = x - 1.4 2.6 B) x = z - 1.4 2.6 C) z = x - 2.5 1.4 D) z = x - 1.4 2.5 105) A variable x has the possible observations shown below. 105) Possible observations of x: -3 -1 0 1 1 2 4 4 5 Find the z-score corresponding to an observed value of x of 5. Round the values of μ and σ to one decimal place. Round your final answer to two decimal places. A) -1.44 B) -1.71 C) 1.44 D) 1.38 Provide an appropriate response. 106) Which score has a higher relative position, a score of 34.5 on a test with a mean of 30 and a standard deviation of 3, or a score of 305.1 on a test with a mean of 270 and a a standard deviation of 27? (Assume that the distributions being compared have approximately the same shape.) A) A score of 34.5 B) A score of 305.1 C) Both scores have the same relative position. 28 106) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 107) For a dayʹs work, Chris is paid $50 to cover expenses plus $16 per hour. Let x denote the number of hours Chris works in a day and let y denote Chrisʹs total salary for the day. Obtain the equation that expresses y in terms of x. Construct a table of values using the x-values 2, 4, and 8 hours. Draw the graph of the equation by plotting the points from the table and connecting them with a straight line. Use the graph to estimate visually Chrisʹs salary for the day if he works 6 hours. 107) y 160 120 80 40 2 4 6 8 x MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine the y-intercept and slope of the linear equation. 108) y = 97.7 - 22.4x A) y-intercept = -22.4, slope = 97.7 C) y-intercept = 22.4, slope = 97.7 108) B) y-intercept = 97.7, slope = -22.4 D) y-intercept = 97.7, slope = 22.4 You are given information about a straight line. Determine whether the line slopes upward, slopes downward, or is horizontal. 109) The equation of the line is y = -14 + 3.8x. 109) A) Slopes downward B) Slopes upward C) Is horizontal 110) The equation of the line is y = 10 - 12x. A) Is horizontal B) Slopes downward C) Slopes upward 110) 111) The equation of the line is y = 4. A) Slopes upward B) Slopes downward C) Is horizontal 112) The y-intercept is -2 and the slope is 0. A) Slopes upward B) Slopes downward C) Is horizontal 113) The y-intercept is -2.7 and the slope is 7. A) Slopes downward B) Is horizontal C) Slopes upward 111) 112) 113) The y-intercept and slope, respectively, of a straight line are given. Find the equation of the line. 114) 0 and -8.9 A) y = 8.9x B) y = 8.9 C) y = -8.9x D) y = -8.9 29 114) 115) -2.7 and 0 A) y = -2.7 B) y = 2.7 C) y = -2.7x D) y - 2.7x = 0 116) -3 and -11 A) y - 11x = -3 B) y = -3 + 11x C) y = -3 - 11x D) y = -3x - 11 115) 116) You are given information about a straight line. Use two points to graph the equation. 117) The equation of the line is y = 7 - 0.5x. 117) y 10 5 -10 -5 5 10 x -5 -10 A) B) y -10 y 10 10 5 5 -5 5 10 x -10 -5 -5 -5 -10 -10 C) 5 10 x 5 10 x D) y -10 y 10 10 5 5 -5 5 10 x -10 -5 -5 -5 -10 -10 30 118) The equation of the line is y = 7. 118) y 10 5 -10 -5 5 10 x -5 -10 A) B) y -10 y 10 10 5 5 -5 5 10 x -10 -5 -5 -5 -10 -10 C) 5 10 x 5 10 x D) y -10 y 10 10 5 5 -5 5 10 x -10 -5 -5 -5 -10 -10 31 119) The y-intercept is -9 and the slope is 0. 119) y 10 5 -10 -5 5 10 x -5 -10 A) B) y -10 y 10 10 5 5 -5 5 10 x -10 -5 -5 -5 -10 -10 C) 5 10 x 5 10 x D) y -10 y 10 10 5 5 -5 5 10 x -10 -5 -5 -5 -10 -10 32 A set of data points and the equations of two lines are given. For each line, determine ∑ e 2 . Then, determine which line fits the set of data points better, according to the least-squares criterion. x 1 2 4 4 120) 120) y 2 3 5 4 Line A: y = 1 + 0.9x Line B: y = 0.8 + 1.1x A) Line A: ∑ e2 = 0.57 B) Line A: ∑ e2 = 0.57 Line B: ∑ e 2 = 1.49 Line A fits the set of data points better. C) Line A: ∑ e 2 = 1.31 Line B: ∑ e2 = 1.49 Line B fits the set of data points better. D) Line A: ∑ e2 = 1.31 Line B: ∑ e2 = 1.57 Line B fits the set of data points better. 121) x y 0 7 1 6 3 5 3 4 Line B: ∑ e 2 = 1.57 Line A fits the set of data points better. 5 2 Line A: y = 7.5 - 0.9x Line B: y = 8.0 - 1.1x A) Line A: ∑ e2 = 2.29 B) Line A: ∑ e2 = 0.87 Line B: ∑ e2 = 2.64 Line B fits the set of data points better. C) Line A: ∑ e2 = 2.29 Line B: ∑ e2 = 0.53 Line B fits the set of data points better. D) Line A: ∑ e2 = 3.12 Line B: ∑ e2 = 2.64 Line A fits the set of data points better. 122) x y 0 1 2 4 4 9 4 11 121) Line B: ∑ e2 = 3.49 Line B fits the set of data points better. 6 14 Line A: y = 1.0 + 2.2x Line B: y = 1.2 + 2.1x A) Line A: ∑ e2 = 6.04 7 15 122) B) Line A: ∑ e2 = 4.86 Line B: ∑ e2 = 5.17 Line B fits the set of data points better. C) Line A: ∑ e2 = 6.04 Line B: ∑ e2 = 4.70 Line A fits the set of data points better. D) Line A: ∑ e2 = 4.86 Line B: ∑ e2 = 5.17 Line A fits the set of data points better. Line B: ∑ e2 = 4.70 Line B fits the set of data points better. Determine the regression equation for the data. Round the final values to three significant digits, if necessary. 123) x 2 4 5 6 123) y 7 11 13 20 ^ A) y = 3x ^ ^ B) y = 0.15 + 3x C) y = 2.8x 33 ^ D) y = 0.15 + 2.8x 124) x 0 3 4 5 12 y 8 2 6 9 12 124) ^ ^ A) y = 4.98 + 0.425x B) y = 4.88 + 0.525x ^ ^ C) y = 4.98 + 0.725x D) y = 4.88 + 0.625x 125) x 6 8 20 28 36 y 2 4 13 20 30 125) ^ ^ A) y = -2.79 + 0.897x B) y = -3.79 + 0.897x ^ ^ C) y = -3.79 + 0.801x D) y = -2.79 + 0.950x 126) x 3 5 7 15 16 y 8 11 7 14 20 126) ^ ^ A) y = 5.07 + 0.850x B) y = 4.07 + 0.753x ^ ^ C) y = 4.07 + 0.850x D) y = 5.07 + 0.753x 127) x 24 26 28 30 32 y 15 13 20 16 24 127) ^ ^ A) y = -11.8 + 0.950x B) y = 11.8 + 1.05x ^ ^ C) y = -11.8 + 1.05x D) y = 11.8 + 0.950x 1 3 5 7 9 128) x y 143 116 100 98 90 ^ 128) ^ A) y = 151 - 6.8x ^ B) y = -140 + 6.2x C) y = -151 + 6.8x ^ D) y = 140 - 6.2x 129) x 1.2 1.4 1.6 1.8 2.0 y 54 53 55 54 56 ^ 129) ^ A) y = 50 + 3x ^ B) y = 50.4 + 2.5x C) y = 54 ^ D) y = 55.3 + 2.4x 130) Ten students in a graduate program were randomly selected. The following data represent their grade point averages (GPAs) at the beginning of the year (x) versus their GPAs at the end of the year (y). x 3.5 3.8 3.6 3.6 3.5 3.9 4.0 3.9 3.5 3.7 y 3.6 3.7 3.9 3.6 3.9 3.8 3.7 3.9 3.8 4.0 ^ ^ A) y = 2.51 + 0.329x B) y = 4.91 + 0.0212x ^ ^ C) y = 5.81 + 0.497x D) y = 3.67 + 0.0313x 34 130) 131) Two different tests are designed to measure employee productivity (x) and dexterity (y). Several employees were randomly selected and tested, and the results are given below. 131) x 23 25 28 21 21 25 26 30 34 36 y 49 53 59 42 47 53 55 63 67 75 ^ ^ A) y = 5.05 + 1.91x B) y = 75.3 - 0.329x ^ ^ C) y = 10.7 + 1.53x D) y = 2.36 + 2.03x 132) Managers rate employees according to job performance (x) and attitude (y). The results for several randomly selected employees are given below. 132) x 59 63 65 69 58 77 76 69 70 64 y 72 67 78 82 75 87 92 83 87 78 ^ ^ A) y = 92.3 - 0.669x B) y = -47.3 + 2.02x ^ ^ C) y = 2.81 + 1.35x D) y = 11.7 + 1.02x The regression equation for the given data points is provided. Graph the regression equation and the data points. x 2 4 5 6 133) 133) y 7 11 13 20 ^ y = 3.0x y 18 12 6 2 6 x 4 A) B) y y 18 18 12 12 6 6 2 4 6 x 2 35 4 6 x C) D) y y 18 18 12 12 6 6 2 x y 134) 3 8 6 x 4 5 11 7 7 2 15 14 4 6 x 16 20 134) ^ y = 5.1 + 0.75x 21 y 18 15 12 9 6 3 2 4 6 8 10 12 14 16 18 20 x A) B) 21 y 21 18 18 15 15 12 12 9 9 6 6 3 3 2 4 6 8 10 12 14 16 18 20 x y 2 36 4 6 8 10 12 14 16 18 20 x C) D) 21 y 21 18 18 15 15 12 12 9 9 6 6 3 3 2 4 6 x y 135) 8 10 12 14 16 18 20 1 73 3 46 x 5 30 y 2 7 28 4 6 8 10 12 14 16 18 20 x 9 20 135) ^ y= 70.4 - 6.2x y 100 90 80 70 60 50 40 30 20 10 1 2 3 4 5 6 7 8 x 9 A) B) y y 100 90 100 90 80 70 80 70 60 50 40 60 50 40 30 20 30 20 10 10 1 2 3 4 5 6 7 8 9 x 1 37 2 3 4 5 6 7 8 9 x C) D) y y 100 90 100 90 80 70 80 70 60 50 60 50 40 30 20 40 30 20 10 10 1 2 3 4 5 6 7 8 9 x 1 2 3 4 5 6 7 8 9 x 136) x 10 14 20 6 6 14 16 24 32 36 y 19 23 29 12 17 23 25 33 37 45 136) ^ y= 9.3 + 0.95x y 40 30 20 10 4 8 12 16 20 24 28 32 36 40 x A) B) y y 40 40 30 30 20 20 10 10 4 8 12 16 20 24 28 32 36 40 x 4 38 8 12 16 20 24 28 32 36 40 x C) D) y y 40 40 30 30 20 20 10 10 4 8 12 16 20 24 28 32 36 40 x 4 8 12 16 20 24 28 32 36 40 x Use the regression equation to predict the y -value corresponding to the given x-value. Round your answer to the nearest tenth. ^ 137) Eight pairs of data yield the regression equation y = 55.8 + 2.79x. Predict y for x = 5.2. A) 57.8 B) 293.0 C) 71.1 D) 70.3 ^ 137) 138) Nine pairs of data yield the regression equation y= 19.4 + 0.93x. Predict y for x = 54. A) 64.7 B) 79.6 C) 69.6 D) 57.8 138) 139) The regression equation relating dexterity scores (x) and productivity scores (y) for ten randomly 139) ^ selected employees of a company is y = 5.50 + 1.91x. Predict the productivity score for an employee whose dexterity score is 32. A) 56.3 B) 58.2 C) 177.9 D) 66.6 140) The regression equation relating attitude rating (x) and job performance rating (y) for ten 140) ^ randomly selected employees of a company is y = 11.7 + 1.02x. Predict the job performance rating for an employee whose attitude rating is 67. A) 12.6 B) 80.0 C) 78.9 D) 80.1 Compute the specified sum of squares. ^ 141) 141) The regression equation for the data below is y = 3.000x. x 2 4 5 6 y 7 11 13 20 SSR A) 78.75 B) 72.45 C) 10.00 D) 88.75 142) The data below consist of test scores (y) and hours of preparation (x) for 5 randomly selected ^ students. The regression equation is y = 44.8447 + 3.52427x. x 5 2 9 6 10 y 64 48 72 73 80 SSR A) 511.724 B) 87.4757 C) 599.200 39 D) 498.103 142) 143) The data below consist of heights (x), in meters, and masses (y), in kilograms, of 6 randomly 143) ^ selected adults. The regression equation is y = -181.342 + 144.46x. x 1.61 1.72 1.78 1.80 1.67 1.88 y 54 62 70 84 61 92 SSR A) 1079.5 B) 979.44 C) 1149.2 D) 100.06 ^ 144) 144) The regression equation for the data below is y = 6.18286 + 4.33937x. x 9 7 2 3 4 22 17 y 43 35 16 21 23 102 81 SSR A) 13.4790 B) 6544.86 C) 6531.37 D) 6421.83 ^ 145) 145) The regression equation for the data below is y = 3.000x. x 2 4 5 6 y 7 11 13 20 SSE A) 10.00 B) 88.75 C) 78.75 D) 14.25 146) The data below consist of test scores (y) and hours of preparation (x) for 5 randomly selected 146) ^ students. The regression equation is y = 44.8447 + 3.52427x. x 5 2 9 6 10 y 64 48 72 73 80 SSE A) 511.724 B) 599.200 C) 87.4757 D) 96.1030 147) The data below consist of heights (x), in meters, and masses (y), in kilograms, of 6 randomly ^ selected adults. The regression equation is y = -181.342 + 144.46x. x 1.61 1.72 1.78 1.80 1.67 1.88 y 54 62 70 84 61 92 SSE A) 119.30 B) 979.44 C) 100.06 40 D) 1079.5 147) ^ 148) 148) The regression equation for the data below is y = 3.000x. x 2 4 5 6 y 7 11 13 20 SST A) 10.00 B) 78.75 C) 92.25 D) 88.75 149) The data below consist of test scores (y) and hours of preparation (x) for 5 randomly selected 149) ^ students. The regression equation is y = 44.8447 + 3.52427x. x 5 2 9 6 10 y 64 48 72 73 80 SST A) 599.200 B) 498.103 C) 511.724 D) 87.4757 150) The data below consist of heights (x), in meters, and masses (y), in kilograms, of 6 randomly 150) ^ selected adults. The regression equation is y = -181.342 + 144.46x. x 1.61 1.72 1.78 1.80 1.67 1.88 y 54 62 70 84 61 92 SST A) 100.06 B) 1079.5 C) 979.44 D) 1119.3 Compute the coefficient of determination. Round your answer to four decimal places. 151) A regression equation is obtained for a set of data points. It is found that the total sum of squares is 26.961, the regression sum of squares is 15.044, and the error sum of squares is 11.917. A) 1.7921 B) 0.7921 C) 0.4420 D) 0.5580 152) A regression equation is obtained for a set of data points. It is found that the total sum of squares is 117.0, the regression sum of squares is 81.5, and the error sum of squares is 35.5. A) 0.3034 B) 0.6966 C) 0.4356 D) 1.4356 ^ B) 0.9420 C) 0.8873 D) 0.7265 154) The test scores (y) of 6 randomly selected students and the numbers of hours they prepared (x) are as follows. x 5 10 4 6 10 9 y 64 86 69 86 59 87 ^ The regression equation is y = 1.06604x + 67.3491. A) -0.2242 B) 0.2242 C) 0.6781 41 152) 153) 153) The regression equation for the data below is y = 3x. x 2 4 5 6 y 7 11 13 20 A) 0.4839 151) D) 0.0503 154) 155) The cost of advertising (x), in thousands of dollars, and the number of products sold (y), in thousands, for eight randomly selected product lines are shown below. 155) x 9 2 3 4 2 5 9 10 y 85 52 55 68 67 86 83 73 ^ The regression equation is y = 2.78846x + 55.7885. A) 0.5009 B) -0.0707 C) 0.2353 D) 0.7077 156) For a particular regression analysis, it is found that SST = 895.0 and SSE = 352.2. A) 0.6065 B) 0.3935 C) 0.7788 D) 2.5412 156) Determine the percentage of variation in the observed values of the response variable that is explained by the regression. Round to the nearest tenth of a percent if needed. 157) x 16.9 34.2 44.8 11.9 18.3 157) y 2 7 4 10 2 A) 12.8% B) 1.4% C) 10.5% D) 11.8% 158) x 5 10 4 6 10 9 y 64 86 69 86 59 87 A) 5.0% 158) B) 22.4% C) 0% 159) x 9 2 3 4 2 5 9 10 y 85 52 55 68 67 86 83 73 A) 70.8% B) 50.1% D) 67.8% 159) C) 23.5% D) 24.6% Solve the problem. 160) The paired data below consist of the temperatures on randomly chosen days and the amount a certain kind of plant grew (in millimeters): x 62 76 50 51 71 46 51 44 79 y 36 39 50 13 33 33 17 6 16 Find the SST. A) 1684 B) 243 C) 0 D) 1864 161) The paired data below consist of the temperatures on randomly chosen days and the amount a certain kind of plant grew (in millimeters): x 62 76 50 51 71 46 51 44 79 y 36 39 50 13 33 33 17 6 16 Find the SSR. A) 242.951 B) 64.328 C) 243 B) 242.951 C) 1619.672 42 161) D) 0 162) The paired data below consist of the temperatures on randomly chosen days and the amount a certain kind of plant grew (in millimeters): x 62 76 50 51 71 46 51 44 79 y 36 39 50 13 33 33 17 6 16 Find the SSE. A) 243 160) D) 1748.328 162) 163) A study was conducted to compare the average time spent in the lab each week versus course grade for computer students. The results are recorded in the table below. Grade (percent) Number of hours spent in lab 10 96 11 51 16 62 9 58 7 89 15 81 16 46 10 51 Find the coefficient of determination. A) 0.462 B) 0.335 C) 0.017 163) D) 0.112 164) A study was conducted to compare the average time spent in the lab each week versus course grade for computer students. The results are recorded in the table below. Grade (percent) Number of hours spent in lab 10 96 11 51 16 62 9 58 7 89 15 81 16 46 10 51 164) Determine the percentage of variation in the observed values of the response variable explained by the regression.. A) 0.335% B) 0.112% C) 33.5% D) 11.2% 165) A study was conducted to compare the average time spent in the lab each week versus course grade for computer students. The results are recorded in the table below. Grade (percent) Number of hours spent in lab 10 96 11 51 16 62 9 58 7 89 15 81 16 46 10 51 State how useful the regression equation appears to be for making predictions. A) Not very useful B) Extremely useful C) Moderately useful D) Not enough information 43 165) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 166) For a particular regression analysis, the following regression equation is obtained: 166) ^ y = 2.12 + 0.56x. Furthermore, the coefficient of determination is 0.024. How useful would the regression equation be for making predictions? How can you tell? MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 167) True or false? In the context of regression analysis, the coefficient of determination is the proportion of variation in the observed values of the response variable not explained by the regression A) True B) False 167) 168) True or false? In the context of regression analysis, the regression sum of squares is the variation in the observed values of the response variable explained by the regression. A) True B) False 168) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 169) For a particular regression analysis, it is found that SST = 924.5 and SSE = 807.5. Does the regression equation appear to be useful for making predictions? How can you tell? 169) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 170) True or false? In the context of regression analysis, if the regression sum of squares is large relative to the error sum of squares, then the regression equation is useful for making predictions. A) True B) False 170) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 171) When performing regression analysis, how can you evaluate how useful the regression equation is for making predictions? 171) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. ^ 172) For a particular regression analysis, the following regression equation is obtained: y = 8.3x + 32, where x represents the number of hours studied for a test and y represents the score on the test. True or false? If the coefficient of determination is 0.976, the number of hours studied is very useful for predicting the test score. A) True B) False Obtain the linear correlation coefficient for the data. Round your answer to three decimal places. 173) x 34.0 22.4 10.8 38.3 31.3 y 8 6 5 7 2 A) 0.249 B) -0.249 C) 0 D) -0.222 174) x 57 53 59 61 53 56 60 y 156 164 163 177 159 175 151 A) 0.109 B) -0.078 172) 173) 174) C) -0.054 44 D) 0.214 175) x 62 53 64 52 52 54 58 y 158 176 151 164 164 174 162 A) 0.507 B) 0.754 175) C) -0.081 D) -0.775 176) The data below show the test scores (y) of 6 randomly selected students and the number of hours (x) they studied for the test. x 5 10 4 6 10 9 y 64 86 69 86 59 87 A) 0.678 B) -0.678 C) 0.224 D) -0.224 177) The data below show the cost of advertising (x), in thousands of dollars, and the number of products sold (y), in thousands, for each of eight randomly selected product lines. x 9 2 3 4 2 5 9 10 y 85 52 55 68 67 86 83 73 A) 0.246 B) -0.071 C) 0.235 176) 177) D) 0.708 178) A study was conducted to compare the number of hours spent in the computer lab on an assignment (x) and the grade on the assignment (y), for each of eight randomly selected students in a computer class. The results are recorded in the table below. 178) x y 10 96 11 51 16 62 9 58 7 89 15 81 16 46 10 51 A) -0.284 B) 0.462 C) 0.017 D) -0.335 179) Managers rate employees according to job performance (x) and attitude (y). The results for several randomly selected employees are given below. x 59 63 65 69 58 77 76 69 70 64 y 72 67 78 82 75 87 92 83 87 78 A) 0.863 B) 0.610 C) 0.729 D) 0.916 180) Two separate tests, x and y, are designed to measure a studentʹs ability to solve problems. Several students are randomly selected to take both tests and their results are shown below. x 48 52 58 44 43 43 40 51 59 y 73 67 73 59 58 56 58 64 74 A) 0.714 B) 0.109 C) 0.867 45 179) D) 0.548 180) 181) The data below show the temperature (x) and the amount a plant grew (y), in millimeters, for each of nine randomly selected days. Calculate the linear correlation coefficient r. Can you conclude from the value of r alone that the variables x and y are unrelated? x 62 76 50 51 71 46 51 44 79 y 36 39 50 13 33 33 17 6 16 A) 0.196; Yes B) 0.196; No C) 0.038; No D) 0.038; Yes 182) Two different tests are designed to measure employee productivity (x) and dexterity (y). Several employees are randomly selected and tested with these results. Calculate the linear correlation coefficient r. Can you conclude from the value of r alone that the variables x and y are linearly related? x 23 25 28 21 21 25 26 30 34 36 y 49 53 59 42 47 53 55 63 67 75 A) 0.986; Yes B) 0.986; No C) 0.972 No 183) y x x C) D) y y x x 46 182) D) 0.972;Yes Provide an appropriate response. 183) Determine which plot shows the strongest linear correlation. B) A) y 181) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 184) What is the relationship between the linear correlation coefficient and the usefulness of the regression equation for making predictions? 184) 185) Create a scatter diagram that shows a perfect positive linear correlation between x and y. How would the scatter diagram change if the correlation showed each of the following? (a) a strong positive linear correlation; (b) a weak positive linear correlation; (c) no linear correlation. 185) 186) Suppose data are collected for each of several randomly selected adults for height, in inches, and number of calories burned in 30 minutes of walking on a treadmill at 3.5 mph. How would the value of the linear correlation coefficient, r, change if all of the heights were converted to meters? 186) 187) Explain why having a high linear correlation does not imply causality. Give an example to support your answer. 187) 188) The variables height and weight could reasonably be expected to have a positive linear correlation coefficient, since taller people tend to be heavier, on average, than shorter people. Give an example of a pair of variables which you would expect to have a negative linear correlation coefficient and explain why. Then give an example of a pair of variables whose linear correlation coefficient is likely to be close to zero. 188) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 189) Which of the following statements concerning the linear correlation coefficient are true? 189) A: If the linear correlation coefficient for two variables is zero, then there is no relationship between the variables. B: If the slope of the regression line is negative, then the linear correlation coefficient is negative. C: The value of the linear correlation coefficient always lies between -1 and 1. D: A linear correlation coefficient of 0.62 suggests a stronger linear relationship than a linear correlation coefficient of -0.82. A) A and D B) A and B C) C and D D) B and C SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 190) For each of 200 randomly selected cities, Pete compared data for the number of churches in the city (x) and the number of homicides in the past decade (y). He calculated the linear correlation coefficient and was surprised to find a strong positive linear correlation for the two variables. Does this suggest that when a city builds new churches this will tend to cause an increase in the number of homicides? Why do you think that a strong positive linear correlation coefficient was obtained? 47 190) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the indicated probability. 191) If you flip a coin three times, the possible outcomes are HHH HHT HTH HTT THH THT TTH TTT. What is the probability of getting at least one head? 7 1 3 1 B) C) D) A) 8 2 4 4 191) 192) If you flip a coin three times, the possible outcomes are HHH HHT HTH HTT THH THT TTH TTT. What is the probability of getting at least two tails? 1 1 5 3 A) B) C) D) 2 8 8 8 192) 193) If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. What is the probability that the first two tosses come up the same? 3 1 1 1 B) C) D) A) 8 2 8 4 193) 194) If two balanced die are rolled, the possible outcomes can be represented as follows. 194) (1, 1) (2, 1) (3, 1) (4, 1) (5, 1) (6, 1) (1, 2) (2, 2) (3, 2) (4, 2) (5, 2) (6, 2) (1, 3) (2, 3) (3, 3) (4, 3) (5, 3) (6, 3) (1, 4) (2, 4) (3, 4) (4, 4) (5, 4) (6, 4) (1, 5) (2, 5) (3, 5) (4, 5) (5, 5) (6, 5) (1, 6) (2, 6) (3, 6) (4, 6) (5, 6) (6, 6) Determine the probability that the sum of the dice is 9. 1 1 1 B) C) A) 6 12 9 D) 5 36 195) If two balanced die are rolled, the possible outcomes can be represented as follows. 195) (1, 1) (2, 1) (3, 1) (4, 1) (5, 1) (6, 1) (1, 2) (2, 2) (3, 2) (4, 2) (5, 2) (6, 2) (1, 3) (2, 3) (3, 3) (4, 3) (5, 3) (6, 3) (1, 4) (2, 4) (3, 4) (4, 4) (5, 4) (6, 4) (1, 5) (2, 5) (3, 5) (4, 5) (5, 5) (6, 5) (1, 6) (2, 6) (3, 6) (4, 6) (5, 6) (6, 6) Determine the probability that the sum of the dice is 4 or 10. 7 2 5 B) C) A) 36 9 36 48 D) 1 6 196) A committee of three people is to be formed. The three people will be selected from a list of five possible committee members. A simple random sample of three people is taken, without replacement, from the group of five people. If the five people are represented by the letters A, B, C, D, E, the possible outcomes are as follows. 196) ABC ABD ABE ACD ACE ADE BCD BCE BDE CDE Determine the probability that C and D are both included in the sample. 3 1 2 B) C) A) 10 10 5 D) 2 10 197) A committee of three people is to be formed. The three people will be selected from a list of five possible committee members. A simple random sample of three people is taken, without replacement, from the group of five people. Using the letters A, B, C, D, E to represent the five people, list the possible samples of size three and use your list to determine the probability that B is included in the sample. (Hint: There are 10 possible samples.) 1 7 B) A) 2 10 C) 3 5 D) 2 5 198) Sammy and Sally each carry a bag containing a banana, a chocolate bar, and a licorice stick. Simultaneously, they take out a single food item and consume it. The possible pairs of food items that Sally and Sammy consumed are as follows. chocolate bar - chocolate bar licorice stick - chocolate bar banana - banana chocolate bar - licorice stick licorice stick - licorice stick chocolate bar - banana banana - licorice stick licorice stick - banana banana - chocolate bar Find the probability that at least one chocolate bar was eaten. 7 5 4 B) C) A) 9 9 5 49 D) 197) 1 3 198) 199) A bag contains four chips of different colors, including red, blue, green, and yellow. A chip is selected at random from the bag and then replaced in the bag. A second chip is then selected at random. Make a list of the possible outcomes (for example RB represents the outcome red chip followed by blue chip) and use your list to determine the probability that the two chips selected are the same color. (Hint: There are 16 possible outcomes.) 1 1 B) A) 8 4 C) 1 16 D) 1 2 200) A bag contains four chips of different colors, including red, blue, green, and yellow. A chip is selected at random from the bag and then replaced in the bag. A second chip is then selected at random. Make a list of the possible outcomes (for example RB represents the outcome red chip followed by blue chip) and use your list to determine the probability that one blue chip and one yellow chip are selected. 1 1 1 1 B) C) D) A) 2 16 4 8 Estimate the probability of the event. 201) A polling firm, hired to estimate the likelihood of the passage of an up-coming referendum, obtained the set of survey responses to make its estimate. The encoding system for the data is: 1 = FOR, 2 = AGAINST. If the referendum were held today, find the probability that it would pass. 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1 A) 0.6 B) 0.65 C) 0.5 199) 200) 201) D) 0.4 202) The data set represents the income levels of the members of a country club. Find the probability that a randomly selected member earns at least $92,000. Round your answers to the nearest tenth. 202) 98,000 104,000 84,000 107,000 88,000 98,000 92,000 76,000 113,000 128,000 80,000 95,000 110,000 88,000 104,000 101,000 92,000 116,000 72,000 101,000 A) 0.8 B) 0.4 C) 0.7 D) 0.6 203) In a certain class of students, there are 10 boys from Wilmette, 5 girls from Kenilworth, 10 girls from Wilmette, 7 boys from Glencoe, 5 boys from Kenilworth and 6 girls from Glencoe. If the teacher calls upon a student to answer a question, what is the probability that the student will be from Kenilworth? A) 0.116 B) 0.233 C) 0.313 D) 0.227 203) 204) The following frequency distribution analyzes the scores on a math test. Find the probability that a score greater than 82 was achieved. 204) A) 0.813 B) 0.625 C) 0.188 50 D) 0.375 205) A frequency distribution on employment information from Alpha Corporation follows.. Find the probability that an employee has been with the company 10 years or less. 205) Years Employed No. of Employees 1-5 6-10 11-15 16-20 21-25 26-30 A) 0.368 5 20 25 10 5 3 B) 0.294 C) 0.735 D) 0.632 Answer the question. 206) Find the odds against correctly guessing the answer to a multiple choice question with 5 possible answers. A) 4 to 1 B) 5 to 1 C) 5 to 4 D) 4 to 5 206) 207) In a certain town, 25% of people commute to work by bicycle. If a person is selected randomly from the town, what are the odds against selecting someone who commutes by bicycle? A) 1 to 4 B) 3 to 4 C) 3 to 1 D) 1 to 3 207) 208) Suppose you are playing a game of chance. If you bet $4 on a certain event, you will collect $92 (including your $4 bet) if you win. Find the odds used for determining the payoff. A) 23 to 1 B) 22 to 1 C) 1 to 22 D) 92 to 96 208) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 209) Discuss the range of possible values for probabilities. Give examples to support each. 210) On an exam question asking for a probability, Sue had an answer of 13 . Explain how she 8 209) 210) knew that this result was incorrect. 211) Describe an event whose probability of occurring is 1 and explain what that probability means. Describe an event whose probability of occurring is 0 and explain what that probability means. 211) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 212) 212) Which of the following could not possibly be probabilities? A. -0.31 8 B. 7 C. 0 D. 0.71 A) A and C B) A and B C) A and D 51 D) B and C 213) When a balanced die is rolled, the probability that the number that comes up will be a one is 1 . 6 213) This means that if the die is rolled 36 times, a one will show up six times. A) True B) False SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 214) Interpret the following probability statement using the frequentist interpretation of probability. The probability is 0.83 that this particular type of surgery will be successful. 214) 215) Suppose that you roll a die and record the number that comes up and then flip a coin and record whether it comes up heads or tails. One possible outcome can be represented as 2H (a two on the die followed by heads). Make a list of all the possible outcomes. What is the probability that you get tails and an even number? What assumption are you making when you find this probability? 215) 216) Suppose that in an election for governor of Oregon there are five candidates of whom two are women. A statistics student reasons as follows. The probability that a woman will win 2 f the election is equal to which is . What is wrong with his reasoning? 5 N 216) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. List the outcomes comprising the specified event. 217) Three board members for a nonprofit organization will be selected from a group of five people. The board members will be selected by drawing names from a hat. The names of the five possible board members are Allison, Betty, Charlie, Dave, and Emily. The possible outcomes can be represented as follows. ABC ADE ABD BCD ABE BCE ACD BDE ACE CDE Here, for example, ABC represents the outcome that Allison, Betty, and Charlie are selected to be on the board. List the outcomes that comprise the following event. A = event that Charlie is selected A) ABC, ACD, ACE, BCD, BCE, CDE C) CDE B) ABC, ACD, ACE, BCD, CDE D) ABC, ACD, ACE, BCD, BCE, CDE, BDE 52 217) 218) When a quarter is tossed four times, 16 outcomes are possible. HHHH HTHH THHH TTHH HHHT HTHT THHT TTHT HHTH HTTH THTH TTTH 218) HHTT HTTT THTT TTTT Here, for example, HTTH represents the outcome that the first toss is heads, the next two tosses are tails, and the fourth toss is heads. List the outcomes that comprise the following event. A = event the first three tosses come up the same A) HHHT, TTTH C) HHHT, TTTH, HTTT, THHH B) HHHH, HHHT, TTTH, TTTT D) HHH, TTT 219) In a competition, two people will be selected from four finalists to receive the first and second prizes. The prize winners will be selected by drawing names from a hat. The names of the four finalists are Jim, George, Helen, and Maggie. The possible outcomes can be represented as follows. JG JH JM GJ HJ HG HM MJ 219) GH GM MG MH Here, for example, JG represents the outcome that Jim receives the first prize and George receives the second prize. List the outcomes that comprise the following event. A = event that both prize winners are women A) HJ, HM, MH C) HM B) HM, MH, HG, MG D) HM, MH List the outcome(s) of the stated event. 220) The odds against winning in a horse race are shown in the following table. 220) Horse #1 #2 #3 #4 #5 #6 #7 Odds 8 16 1 20 10 16 20 Based on these odds, which horses comprise: A = event one of the top two favorites wins the race? A) Horses #4 and #7 B) Horses #1 and #2 C) Horse #3 D) Horses #1 and #3 221) The odds against winning in a horse race are shown in the following table. Horse #1 #2 #3 #4 #5 #6 #7 Odds 2 16 2 18 9 18 5 Based on these odds, which horses comprise: A = event one of the two long shots (least likely to win) wins the race? A) Horses #4 and #6 B) Horse #1 C) Horses #1 and #2 D) Horses #1 and #3 53 221) 222) The odds against winning in a horse race are shown in the following table. 222) Horse #1 #2 #3 #4 #5 #6 #7 Odds 8 14 1 18 12 18 1 Based on these odds, which horses comprise: A = event the winning horseʹs number is above 4? A) Horses #1, #2, #4, #5, and #6 B) Horses #5, #6, and #7 C) Horses #4, #5, #6, and #7 D) Horse #7 List the outcomes comprising the specified event. 223) When a quarter is tossed four times, 16 outcomes are possible. HHHH HTHH THHH TTHH HHHT HTHT THHT TTHT HHTH HTTH THTH TTTH 223) HHTT HTTT THTT TTTT Here, for example, HTTH represents the outcome that the first toss is heads, the next two tosses are tails, and the fourth toss is heads. The event A is defined as follows. A = event the first two tosses are heads List the outcomes that comprise the event (not A). A) HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT B) HHHH, HHHT, HHTH, HHTT C) TTHH, TTHT, TTTH, TTTT D) THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT 224) When a quarter is tossed four times, 16 outcomes are possible. HHHH HTHH THHH TTHH HHHT HTHT THHT TTHT HHTH HTTH THTH TTTH HHTT HTTT THTT TTTT Here, for example, HTTH represents the outcome that the first toss is heads, the next two tosses are tails, and the fourth toss is heads. The events A and B are defined as follows. A = event exactly two tails are tossed B = event the first and last tosses are the same List the outcomes that comprise the event (A & B). A) HTTH, THHT B) HHHH, HHTH, HTHH, HTTH, THHT, THTT, TTHT, TTTT C) HHTT, HTHT, HTTH, THHT, THTH, TTHH D) HHHH, HHTH, HHTT, HTHH, HTHT, HTTH, THHT, THTH, THTT, TTHH, TTHT, TTTT 54 224) 225) When a quarter is tossed four times, 16 outcomes are possible. HHHH HTHH THHH TTHH HHHT HTHT THHT TTHT HHTH HTTH THTH TTTH 225) HHTT HTTT THTT TTTT Here, for example, HTTH represents the outcome that the first toss is heads, the next two tosses are tails, and the fourth toss is heads. The events A and B are defined as follows. A = event exactly two tails are tossed B = event the first and last tosses are the same List the outcomes that comprise the event (A or B). A) HTTH, THHT B) HHHH, HHTH, HHTT, HTHH, HTHT, HTTH, THHT, THTH, THTT, TTHH, TTHT, TTTT C) HHTT, HTHT, HTTH, THHT, THTH, TTHH D) HHHH, HHTH, HTHH, HTTH, THHT, THTT, TTHT, TTTT 226) Three board members for a nonprofit organization will be selected from a group of five people. The board members will be selected by drawing names from a hat. The names of the five possible board members are Allison, Bob, Charlie, Dave, and Emily. The possible outcomes can be represented as follows. ABC ADE ABD BCD ABE BCE ACD BDE ACE CDE Here, for example, ABC represents the outcome that Allison, Bob, and Charlie are selected to be on the board. The event A is defined as follows. A = event that Bob and Dave are both selected List the outcomes that comprise the event (not A). A) ABC, ABE, ACD, ACE, ADE, BCE, CDE C) ABD, BCD, BDE B) ABC, ABE, ACE, ADE, BCE, CDE D) ACE 55 226) 227) Three board members for a nonprofit organization will be selected from a group of five people. The board members will be selected by drawing names from a hat. The names of the five possible board members are Allison, Bob, Charlie, Dave, and Emily. The possible outcomes can be represented as follows. ABC ADE ABD BCD ABE BCE ACD BDE 227) ACE CDE Here, for example, ABC represents the outcome that Allison, Bob, and Charlie are selected to be on the board. The events A and B are defined as follows. A = event that Dave is selected B = event that fewer than two men are selected List the outcomes that comprise the event (A & B). A) ABD, ADE, BDE, ABC, ACE, BCE C) ABD, ADE, BDE, BCD, ACD, CDE B) ABE, ABD, ADE, BDE D) ABD, ADE, BDE 228) Three board members for a nonprofit organization will be selected from a group of five people. The board members will be selected by drawing names from a hat. The names of the five possible board members are Allison, Betty, Charlie, Dave, and Emily. The possible outcomes can be represented as follows. ABC ADE ABD BCD ABE BCE ACD BDE ACE CDE Here, for example, ABC represents the outcome that Allison, Betty, and Charlie are selected to be on the board. The events A and B are defined as follows. A = event that Dave is selected B = event that Allison is selected List the outcomes that comprise the event (A or B). A) ABC, ABD, ABE, ACD, ACE, ADE, BCD, BDE B) ABC, ABD, ABE, ACD, ACE, ADE, BCD, BDE, CDE C) ABD, ACD, ADE D) ABC, ABE, ACE, BCD, BDE, CDE 56 228) 229) In a competition, two people will be selected from four finalists to receive the first and second prizes. The prize winners will be selected by drawing names from a hat. The names of the four finalists are Jim, George, Helen, and Maggie. The possible outcomes can be represented as follows. JG HJ JH JM GJ HG HM MJ 229) GH GM MG MH Here, for example, JG represents the outcome that Jim receives the first prize and George receives the second prize. The event A is defined as follows. A = event that Helen gets first prize List the outcomes that comprise the event (not A). A) JG, JH, JM, GJ, GH, GM, MJ C) HJ, HG, HM B) JG, JM, GJ, GM, MJ, MG D) JG, JH, JM, GJ, GH, GM, MJ, MG, MH 230) In a competition, two people will be selected from four finalists to receive the first and second prizes. The prize winners will be selected by drawing names from a hat. The names of the four finalists are Jim, George, Helen, and Maggie. The possible outcomes can be represented as follows. JG HJ JH JM GJ HG HM MJ 230) GH GM MG MH Here, for example, JG represents the outcome that Jim receives the first prize and George receives the second prize. The events A and B are defined as follows. A = event that Helen gets first prize B = event that George gets a prize List the outcomes that comprise the event (A or B). A) HG B) JG, GJ, GH, GM, HJ, HM, MG C) JG, GJ, GH, GM, HJ, HG, HM, MG D) JG, JH, GJ, GH, GM, HJ, HG, HM, MG, MH 231) In a competition, two people will be selected from four finalists to receive the first and second prizes. The prize winners will be selected by drawing names from a hat. The names of the four finalists are Jim, George, Helen, and Maggie. The possible outcomes can be represented as follows. JG HJ JH JM GJ HG HM MJ GH GM MG MH Here, for example, JG represents the outcome that Jim receives the first prize and George receives the second prize. The events A and B are defined as follows. A = event that Helen gets first prize B = event that both prize winners are women List the outcomes that comprise the event (A & B). A) HJ, HG, HM C) HM B) HJ, HG, HM, MH D) HM, MH 57 231) Describe the specified event in words. 232) The number of hours needed by sixth grade students to complete a research project was recorded with the following results. Hours Number of students (f) 4 15 5 11 6 19 7 6 8 9 9 16 10 2 232) A student is selected at random. The event A is defined as follows. A = the event the student took at least 8 hours Describe the event (not A) in words. A) The event the student took at most 8 hours B) The event the student took more than 8 hours C) The event the student took less than 8 hours D) The event the student did not take 8 hours 233) The number of hours needed by sixth grade students to complete a research project was recorded with the following results. Hours Number of students (f) 4 15 5 11 6 19 7 6 8 9 9 16 10 2 A student is selected at random. The event A is defined as follows. A = the event the student took between 5 and 9 hours inclusive B = the event the student took at least 7 hours Describe the event (A & B) in words. A) The event the student took between 5 and 7 hours inclusive B) The event the student took between 7 and 9 hours inclusive C) The event the student at least 5 hours D) The event the student took more than 7 hours and less than 9 hours 58 233) 234) The number of hours needed by sixth grade students to complete a research project was recorded with the following results. Number of students (f) Hours 4 5 5 11 6 19 7 6 8 9 9 16 10 2 234) A student is selected at random. The events A and B are defined as follows. A = the event the student took less than 10 hours B = the event the student took between 9 and 5 hours inclusive Describe the event (A or B) in words. A) The event the student took between 10 and 9 hours inclusive B) The event the student took less than 10 hours or more than 9 hours C) The event the student took less than 10 hours or between 9 and 5 hours inclusive D) The event the student took less than 10 hours and between 9 and 5 hours inclusive Determine the number of outcomes that comprise the specified event. 235) The age distribution of students at a community college is given below. Age (years) Number of students (f) Under 21 2041 21-25 2118 26-30 1167 31-35 845 Over 35 226 235) A student from the community college is selected at random. The event A is defined as follows. A = event the student is between 26 and 35 inclusive. Determine the number of outcomes that comprise the event (not A). A) 4159 B) 2012 C) 4385 59 D) 5230 236) The age distribution of students at a community college is given below. Age (years) Number of students (f) Under 21 2063 21-25 2142 26-30 1158 31-35 880 Over 35 204 236) A student from the community college is selected at random. The event A is defined as follows. A = event the student is under 31 Determine the number of outcomes that comprise the event (not A). A) 1084 B) 880 C) 5363 D) 204 237) 237) The age distribution of students at a community college is given below. Age (years) Number of students (f) Under 21 2196 21-25 2057 26-30 1179 31-35 832 Over 35 223 A student from the community college is selected at random. The events A and B are defined as follows. A = event the student is between 21 and 35 inclusive B = event the student is 26 or over Determine the number of outcomes that comprise the event (A & B). A) 6302 B) 4291 C) 2011 D) 2234 238) 238) The age distribution of students at a community college is given below. Age (years) Number of students (f) Under 21 2059 21-25 2139 26-30 1173 31-35 873 Over 35 223 A student from the community college is selected at random. The events A and B are defined as follows. A = event the student is under 21 B = event the student is over 35 Determine the number of outcomes that comprise the event (A & B). A) 2059 B) 2282 C) 4185 60 D) 0 239) 239) The age distribution of students at a community college is given below. Age (years) Number of students (f) Under 21 2076 21-25 2053 26-30 1029 31-35 822 Over 35 203 A student from the community college is selected at random. The events A and B are defined as follows. A = event the student is between 21 and 35 inclusive B = event the student is 26 or over Determine the number of outcomes that comprise the event (A or B). A) 1851 B) 4107 C) 5958 D) 2054 240) The number of hours needed by sixth grade students to complete a research project was recorded with the following results. Number of students (f) Hours 4 20 5 20 6 16 7 11 8 10 9 4 10+ 7 A student is selected at random. The event A is defined as follows. A = the event the student took between 5 and 9 hours inclusive Determine the number of outcomes that comprise the event (not A). A) 7 B) 27 C) 51 61 D) 24 240) 241) The number of hours needed by sixth grade students to complete a research project was recorded with the following results. Number of students (f) Hours 4 27 5 27 6 30 7 12 8 10 9 5 10+ 5 241) A student is selected at random. The event A is defined as follows. A = the event the student took more than 7 hours Determine the number of outcomes that comprise the event (not A). A) 32 B) 20 C) 84 D) 96 242) The number of hours needed by sixth grade students to complete a research project was recorded with the following results. Hours Number of students (f) 4 30 5 21 6 29 7 11 8 10 9 5 10+ 5 A student is selected at random. The events A and B are defined as follows. A = the event the student took at most 8 hours B = the event the student took at least 8 hours Determine the number of outcomes that comprise the event (A & B). A) 10 B) 20 C) 111 62 D) 122 242) 243) The number of hours needed by sixth grade students to complete a research project was recorded with the following results. Number of students (f) Hours 4 16 5 17 6 18 7 14 8 14 9 8 10+ 5 243) A student is selected at random. The events A and B are defined as follows. A = the event the student took at most 8 hours B = the event the student took at least 8 hours Determine the number of outcomes that comprise the event (A or B). A) 14 B) 65 C) 106 D) 92 244) The number of hours needed by sixth grade students to complete a research project was recorded with the following results. Number of students (f) Hours 4 22 5 29 6 23 7 14 8 11 9 8 10+ 6 A student is selected at random. The events A and B are defined as follows. A = the event the student took between 6 and 9 hours inclusive B = the event the student took at most 7 hours Determine the number of outcomes that comprise the event (A or B). A) 107 B) 37 C) 56 63 D) 144 244) Determine whether the events are mutually exclusive. 245) When a quarter is tossed four times, 16 outcomes are possible. HHHH HTHH THHH TTHH HHHT HTHT THHT TTHT HHTH HTTH THTH TTTH 245) HHTT HTTT THTT TTTT Here, for example, HTTH represents the outcome that the first toss is heads, the next two tosses are tails, and the fourth toss is heads. The events A and B are defined as follows. A = event the first two tosses are heads B = event the first and last tosses are the same Are the events A and B mutually exclusive? A) Yes B) No 246) When a quarter is tossed four times, 16 outcomes are possible. HHHH HTHH THHH TTHH HHHT HTHT THHT TTHT HHTH HTTH THTH TTTH 246) HHTT HTTT THTT TTTT Here, for example, HTTH represents the outcome that the first toss is heads, the next two tosses are tails, and the fourth toss is heads. The events A and B are defined as follows. A = event exactly two heads are tossed B = event all four tosses come up the same Are the events A and B mutually exclusive? A) Yes B) No 247) Three board members for a nonprofit organization will be selected from a group of five people. The board members will be selected by drawing names from a hat. The names of the five possible board members are Allison, Betty, Charlie, Dave, and Emily. The possible outcomes can be represented as follows. ABC ADE ABD BCD ABE BCE ACD BDE ACE CDE Here, for example, ABC represents the outcome that Allison, Betty, and Charlie are selected to be on the board. The events A and B are defined as follows. A = event that Betty and Allison are both selected B = event that more than one man is selected Are the events A and B mutually exclusive? A) Yes B) No 64 247) 248) Three board members for a nonprofit organization will be selected from a group of five people. The board members will be selected by drawing names from a hat. The names of the five possible board members are Allison, Betty, Charlie, Dave, and Emily. The possible outcomes can be represented as follows. ABC ADE ABD BCD ABE BCE ACD BDE 248) ACE CDE Here, for example, ABC represents the outcome that Allison, Betty, and Charlie are selected to be on the board. The events A, B, and C are defined as follows. A = event that Dave and Allison are both selected B = event that more than one man is selected C = event that fewer than two women are selected Is the collection of events A, B, and C mutually exclusive? A) Yes B) No 249) A card is selected randomly from a deck of 52. The events A, B, and C are defined as follows. 249) A = event the card selected is a heart B = event the card selected is a club C = event the card selected is an ace Is the collection of events A, B, and C mutually exclusive? A) Yes B) No 250) The number of hours needed by sixth grade students to complete a research project was recorded with the following results. Hours Number of students (f) 4 15 5 11 6 19 7 6 8 9 9 16 10 2 A student is selected at random. The events A and B are defined as follows. A = event the student took at most 8 hours B = event the student took at least 7 hours Are the events A and B mutually exclusive? A) Yes B) No 65 250) 251) The number of hours needed by sixth grade students to complete a research project was recorded with the following results. Number of students (f) Hours 4 15 5 11 6 19 7 6 8 9 9 16 10+ 2 251) A student is selected at random. The events A, B, and C are defined as follows. A = event the student took more than 9 hours B = event the student took less than 6 hours C = event the student took between 7 and 9 hours inclusive Is the collection of events A, B, and C mutually exclusive? A) Yes B) No 252) The age distribution of students at a community college is given below. Number of students (f) Age (years) Under 21 2890 21-24 2190 25-28 1276 29-32 651 33-36 274 37-40 117 Over 40 185 A student from the community college is selected at random. The events A and B are defined as follows. A = event the student is at most 28 B = event the student is at least 40 Are the events A and B mutually exclusive? A) Yes B) No 66 252) 253) The age distribution of students at a community college is given below. Number of students (f) Age (years) Under 21 2890 21-24 2190 25-28 1276 29-32 651 33-36 274 37-40 117 Over 40 185 253) A student from the community college is selected at random. The events A, B, and C are defined as follows. A = event the student is at most 32 B = event the student is at least 37 C = event the student is between 21 and 24 inclusive Is the collection of events A, B, and C mutually exclusive? A) Yes B) No 254) The age distribution of students at a community college is given below. Number of students (f) Age (years) Under 21 2890 21-24 2190 25-28 1276 29-32 651 33-36 274 37-40 117 Over 40 185 254) A student from the community college is selected at random. The events A and B are defined as follows. A = event the student is at most 28 B = event the student is at least 37 Are the events (not A) and B mutually exclusive? A) Yes B) No Find the indicated probability. 255) A sample space consists of 49 separate events that are equally likely. What is the probability of each? 1 D) 49 A) 0 B) 1 C) 49 256) On a multiple choice test, each question has 7 possible answers. If you make a random guess on the first question, what is the probability that you are correct? 1 D) 0 A) 7 B) 1 C) 7 67 255) 256) 257) A 12-sided die is rolled. What is the probability of rolling a number less than 11? 5 11 1 B) C) 10 D) A) 6 12 12 257) 258) A bag contains 6 red marbles, 3 blue marbles, and 7 green marbles. If a marble is randomly selected from the bag, what is the probability that it is blue? 1 1 1 3 B) C) D) A) 3 6 7 16 258) 259) If a person is randomly selected, find the probability that his or her birthday is in May. Ignore leap years. 1 1 31 1 B) C) D) A) 31 365 365 12 259) 260) A class consists of 44 women and 14 men. If a student is randomly selected, what is the probability that the student is a woman? 22 22 7 1 B) C) D) A) 7 29 29 58 260) 261) In a poll, respondents were asked whether they had ever been in a car accident. 362 respondents indicated that they had been in a car accident and 475 respondents said that they had not been in a car accident. If one of these respondents is randomly selected, what is the probability of getting someone who has been in a car accident? A) 0.568 B) 0.762 C) 0.003 D) 0.432 261) 262) The distribution of B.A. degrees conferred by a local college is listed below, by major. 262) Major English Mathematics Chemistry Physics Liberal Arts Business Engineering Frequency 2073 2164 318 856 1358 1676 868 9313 What is the probability that a randomly selected degree is in Engineering? A) 0.0932 B) 0.1028 C) 0.0012 D) 868 263) A survey resulted in the sample data in the given table. If one of the survey respondents is randomly selected, find the probability of getting someone who lives in a flat. Type of accommodation Number House 282 Flat 499 Apartment 518 Other 410 A) 0.384 B) 499 C) 0.002 68 D) 0.292 263) Find the indicated probability by using the special addition rule. 264) The age distribution of students at a community college is given below. Age (years) Number of students (f) Under 21 411 21-25 414 26-30 200 31-35 54 Over 35 23 264) 1102 A student from the community college is selected at random. Find the probability that the student is between 26 and 35 inclusive. Round approximations to three decimal places. A) 0.181 B) 254 C) 0.049 D) 0.230 265) The age distribution of students at a community college is given below. Number of students (f) Age (years) Under 21 400 21-25 415 26-30 211 31-35 55 Over 35 22 265) 1103 A student from the community college is selected at random. Find the probability that the student is at least 31. Round approximations to three decimal places. A) 0.050 B) 0.070 C) 77 D) 0.930 266) A relative frequency distribution is given below for the size of families in one U.S. city. Relative frequency Size 2 0.430 3 0.235 4 0.195 5 0.095 6 0.027 7+ 0.018 A family is selected at random. Find the probability that the size of the family is less than 5. Round approximations to three decimal places. A) 0.430 B) 0.860 C) 0.095 D) 0.525 69 266) 267) A relative frequency distribution is given below for the size of families in one U.S. city. Relative frequency Size 2 0.425 3 0.237 4 0.190 5 0.097 6 0.036 7+ 0.015 267) A family is selected at random. Find the probability that the size of the family is between 2 and 5 inclusive. Round approximations to three decimal places. A) 0.522 B) 0.427 C) 0.949 D) 0.852 268) A percentage distribution is given below for the size of families in one U.S. city. Percentage Size 2 50.5 3 24.0 4 12.2 5 7.6 6 3.8 7+ 1.9 268) A family is selected at random. Find the probability that the size of the family is at most 3. Round approximations to three decimal places. A) 0.745 B) 0.240 C) 0.255 D) 0.505 269) A percentage distribution is given below for the size of families in one U.S. city. Percentage Size 2 41.9 3 20.8 4 19.7 5 11.8 6 3.9 7+ 1.9 A family is selected at random. Find the probability that the size of the family is at least 5. Round approximations to three decimal places. A) 0.824 B) 0.942 C) 0.176 D) 0.058 70 269) 270) The distribution of B.A. degrees conferred by a local college is listed below, by major. Major English Mathematics Chemistry Physics Liberal Arts Business Engineering 270) Frequency 2073 2164 318 856 1358 1676 868 9313 What is the probability that a randomly selected degree is in English or Mathematics? A) 0.455 B) 0.424 C) 0.517 D) 0.010 271) A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing an ace or a 9? 13 5 2 B) C) D) 10 A) 2 13 13 271) 272) Two 6-sided dice are rolled. What is the probability that the sum of the numbers on the dice is 6 or 10? 1 4 4 2 B) C) D) A) 60 9 3 9 272) 273) A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing a face card or a 4? 48 2 4 B) C) 16 D) A) 52 13 13 273) Find the indicated probability by using the complementation rule. 274) The age distribution of students at a community college is given below. Age (years) Number of students (f) Under 21 418 21-24 411 25-28 262 29-32 146 33-36 94 37-40 59 Over 40 92 1482 A student from the community college is selected at random. Find the probability that the student is 21 years or over. Give your answer as a decimal rounded to three decimal places. A) 0.656 B) 0.282 C) 0.277 D) 0.718 71 274) 275) The age distribution of students at a community college is given below. Number of students (f) Age (years) Under 21 406 21-24 418 25-28 266 29-32 147 33-36 90 37-40 56 Over 40 99 275) 1482 A student from the community college is selected at random. Find the probability that the student is under 37 years old. Give your answer as a decimal rounded to three decimal places. A) 0.895 B) 0.038 C) 0.061 D) 0.105 276) A relative frequency distribution is given below for the size of families in one U.S. city. Relative frequency Size 2 0.466 3 0.226 4 0.191 5 0.072 6 0.027 7+ 0.018 276) A family is selected at random. Find the probability that the size of the family is at most 6. Round approximations to three decimal places. A) 0.982 B) 0.027 C) 0.955 D) 0.045 277) A relative frequency distribution is given below for the size of families in one U.S. city. Relative frequency Size 2 0.435 3 0.206 4 0.206 5 0.099 6 0.039 7+ 0.015 A family is selected at random. Find the probability that the size of the family is at least 3. Round approximations to three decimal places. A) 0.641 B) 0.565 C) 0.359 D) 0.206 72 277) 278) A percentage distribution is given below for the size of families in one U.S. city. Percentage Size 2 44.2 3 23.4 4 20.2 5 8.0 6 2.7 7+ 1.5 278) A family is selected at random. Find the probability that the size of the family is 4 or more. Round results to three decimal places. A) 0.878 B) 0.122 C) 0.324 D) 0.202 279) A percentage distribution is given below for the size of families in one U.S. city. Percentage Size 2 45.6 3 22.3 4 20.0 5 7.5 6 2.8 7+ 1.8 279) A family is selected at random. Find the probability that the size of the family is less than 6. Round results to three decimal places. A) 0.028 B) 0.982 C) 0.046 D) 0.954 280) Based on meteorological records, the probability that it will snow in a certain town on January 1st is 0.159. Find the probability that in a given year it will not snow on January 1st in that town. A) 1.159 B) 6.289 C) 0.189 D) 0.841 280) 281) The probability that Luis will pass his statistics test is 0.93. Find the probability that he will fail his statistics test. A) 0.07 B) 1.08 C) 0.47 D) 13.29 281) 282) If a person is randomly selected, find the probability that his or her birthday is not in May. Ignore leap years. A) 0.093 B) 0.915 C) 0.085 D) 0.917 282) 73 283) The distribution of B.A. degrees conferred by a local college is listed below, by major. Major English Mathematics Chemistry Physics Liberal Arts Business Engineering 283) Frequency 2073 2164 318 856 1358 1676 868 9313 What is the probability that a randomly selected degree is not in Mathematics? A) 0.232 B) 0.303 C) 0.768 D) 0.682 Find the indicated probability by using the general addition rule. 284) When two balanced dice are rolled, there are 36 possible outcomes. Find the probability that either doubles are rolled or the sum of the dice is 8. 1 1 11 5 B) C) D) A) 4 36 36 18 285) For a person selected randomly from a certain population, events A and B are defined as follows. 284) 285) A = event the person is male B = event the person is a smoker For this particular population, it is found that P(A) = 0.50, P(B) = 0.28, and P(A & B) = 0.15. Find P(A or B). Round approximations to two decimal places. A) 0.48 B) 0.93 C) 0.63 D) 0.78 286) In one city, 50.8% of adults are female, 9.6% of adults are left-handed, and 5.1% are left-handed females. For an adult selected at random from the city, let 286) F = event the person is female L = event the person is left-handed. Find P(F or L). Round approximations to three decimal places. A) 0.553 B) 0.502 C) 0.604 287) Let A and B be events such that P(A) = Determine P(A & B). 59 A) 72 B) D) 0.700 7 2 29 , P(B) = , and P(A or B) = . 36 9 72 5 12 C) 7 162 287) D) 1 72 1 1 1 288) Let A and B be events such that P(A) = , P(A or B) = , and P(A and B) = . Determine P(B). 2 8 7 A) 5 14 B) 43 56 C) 74 1 56 D) 27 56 288) 289) A lottery game has balls numbered 1 through 21. What is the probability of selecting an even numbered ball or the number 8 ball? 21 8 10 B) C) 10 D) A) 8 21 21 289) 290) A spinner has regions numbered 1 through 15. What is the probability that the spinner will stop on an even number or a multiple of 3? 1 2 7 C) D) A) 12 B) 3 3 9 290) 291) If you pick a card at random from a well shuffled deck, what is the probability that you get a face card or a spade? 9 11 25 1 B) C) D) A) 26 26 52 22 291) 292) Of the 57 people who answered ʺyesʺ to a question, 9 were male. Of the 91 people who answered ʺnoʺ to the question, 15 were male. If one person is selected at random from the group, what is the probability that the person answered ʺyesʺ or was male? A) 0.547 B) 0.162 C) 0.486 D) 0.158 292) 293) The manager of a bank recorded the amount of time each customer spent waiting in line during peak business hours one Monday. The frequency table below summarizes the results. 293) Waiting Time Number of (minutes) Customers 0-3 12 4-7 13 8-11 12 12-15 7 16-19 5 20-23 1 24-27 1 If we randomly select one of the times represented in the table, what is the probability that it is at least 12 minutes or between 8 and 15 minutes? A) 0.51 B) 0.647 C) 0.76 D) 0.137 Determine the possible values of the random variable. 294) Suppose a coin is tossed four times. Let X denote the total number of tails obtained in the four tosses. What are the possible values of the random variable X? A) 0, 1, 2, 3, 4 B) 1, 2, 3, 4 C) 1, 2, 3 D) HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT 295) Suppose that two balanced dice are rolled. Let X denote the absolute value of the difference of the two numbers. What are the possible values of the random variable X? A) 0, 1, 2, 3, 4, 5 B) 1, 2, 3, 4, 5 D) 0, 1, 2, 3, 4, 5, 6 C) -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 75 294) 295) 296) Suppose that two balanced dice are rolled. Let Y denote the product of the two numbers. What are the possible values of the random variable Y? A) 2, 3, 4, 5, 6, 8, 10, 12, 15, 18, 20, 24, 30 B) 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 36 C) (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6) D) 0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 36 296) 297) Suppose that two balanced dice, a red die and a green die, are rolled. Let Y denote the value of G - R where G represents the number on the green die and R represents the number on the red die. What are the possible values of the random variable Y? B) 0, 1, 2, 3, 4, 5 A) -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 C) 0, 1, 2, 3, 4, 5, 6 D) -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6 297) 298) For a randomly selected student in a particular high school, let Y denote the number of living grandparents of the student. What are the possible values of the random variable Y? A) 0, 1, 2, 3, 4 B) 4 C) 1, 2, 3, 4 D) 0, 1, 2 298) 299) The following table displays a frequency distribution for the number of siblings for students in one middle school. For a randomly selected student in the school, let X denote the number of siblings of the student. What are the possible values of the random variable X? 299) Number of siblings 0 1 2 3 4 5 6 7 Frequency 189 245 102 42 24 13 5 2 A) Brother, sister C) 0, 1, 2, 3, 4, 5, 6, 7 B) 189, 245, 102, 42, 24, 13, 5, 2 D) 7 300) The following frequency distribution analyzes the scores on a math test. For a randomly selected score between 40 and 99, let Y denote the number of students with that score on the test. What are the possible values of the random variable Y? A) 2, 4, 6, 5 B) 32 C) 2, 4, 6, 15, 5 76 D) 2, 4, 6, 15 300) 301) The following frequency distribution lists the annual household incomes (in thousands of dollars) of one neighborhood in a large city. For a randomly selected income between $200,000 and $700,000, let Y denote the number of households with that income. What are the possible values of the random variable Y? Incomes Frequency 200-300 68 301-400 60 401-500 72 501-600 79 601-700 20 A) 20 C) 68, 60, 72, 79 301) B) 68, 60, 72, 79 , 20 D) 299 Use random-variable notation to represent the event. 302) Suppose a coin is tossed four times. Let X denote the total number of tails obtained in the four tosses. Use random-variable notation to represent the event that the total number of tails is three. A) {X = 3} B) HTTT, THTT, TTHT, TTTH C) {X ≥ 3} D) P{X = 3} 302) 303) Suppose that two balanced dice are rolled. Let X denote the absolute value of the difference of the two numbers. Use random-variable notation to represent the event that the absolute value of the difference of the two numbers is 2. A) {X = 2} B) {(1, 3), (2, 4), (3, 5), (4, 6), (3, 1), (4, 2), (5, 3), (6, 4)} C) P{X = 2} D) X = 2 303) 304) Suppose that two balanced dice are rolled. Let Y denote the product of the two numbers. Use random-variable notation to represent the event that the product of the two numbers is greater than 4. A) {Y > 4} B) {XY > 4} C) {5, 6} D) P{Y > 4} 304) 305) Suppose that two balanced dice are rolled. Let Y denote the sum of the two numbers. Use random-variable notation to represent the event that the sum of the two numbers is at least 11. A) {X+Y ≥ 11} B) {Y > 11} C) {Y ≥ 11} D) (5, 6), (6, 5), (6,6) 305) 306) Suppose that two balanced dice are rolled. Let Y denote the sum of the two numbers. Use random-variable notation to represent the event that the sum of the two numbers is at least 3 but less than 5. A) {3 < Y < 5} B) {3 ≤ Y < 5} C) {3 ≤ X+Y < 5} D) (1, 2), (2, 1), (1, 3), (3, 1), (2, 2) 306) 307) Suppose that two balanced dice are rolled. Let X denote the sum of the two numbers. Use random-variable notation to represent the event that the sum of the two numbers is less than 4. A) (1, 1), (1, 2), (2, 1) B) {X ≤ 4} C) {X+Y < 4} D) {X < 4} 307) 77 308) For a randomly selected student in a particular high school, let Y denote the number of living grandparents of the student. Use random-variable notation to represent the event that the student obtained has exactly three living grandparents. A) {Y ≥ 3} B) {Y = 3} C) {Y < 3} D) P{Y = 3} 308) 309) For a randomly selected student in a particular high school, let Y denote the number of living grandparents of the student. Use random-variable notation to represent the event that the student obtained has at least two living grandparents. A) {Y ≥ 2} B) P{Y ≥ 2} C) {Y > 2} D) {2, 3, 4} 309) 310) The following table displays a frequency distribution for the number of siblings for students in one middle school. For a randomly selected student in the school, let X denote the number of siblings of the student. 310) Number of siblings 0 1 2 3 4 5 6 7 Frequency 189 245 102 42 24 13 5 2 Use random-variable notation to represent the event that the student obtained has fewer than two siblings. A) {X ≤ 2} B) {0, 1} C) {X < 2} D) P{X < 2} 311) The following table displays a frequency distribution for the number of siblings for students in one middle school. For a randomly selected student in the school, let Y denote the number of siblings of the student. 311) Number of siblings 0 1 2 3 4 5 6 7 Frequency 189 245 102 42 24 13 5 2 Use random-variable notation to represent the event that the student obtained has at least two but fewer than six siblings. A) {2 ≤ Y < 6} B) {2 < Y < 6} C) {2 ≤ Y ≤ 6} D) {2, 3, 4, 5} Obtain the probability distribution of the random variable. 312) When a coin is tossed four times, sixteen equally likely outcomes are possible as shown below: HHHH HHHT HHTH HHTT HTHH HTHT HTTH HTTT THHH THHT THTH THTT TTHH TTHT TTTH TTTT Let X denote the total number of tails obtained in the four tosses. Find the probability distribution of the random variable X. Leave your probabilities in fraction form. A) B) C) D) x P(X = x) x P(X = x) x P(X = x) x P(X = x) 0 1/16 1 1/4 0 1/16 0 1/16 1 3/16 2 7/16 1 1/8 1 1/4 2 1/2 3 1/4 2 3/8 2 3/8 3 3/16 4 1/16 3 1/8 3 1/4 4 1/16 4 1/16 4 1/16 78 312) 313) When two balanced dice are rolled, 36 equally likely outcomes are possible as shown below. 313) (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6) (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6) (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6) (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6) (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6) Let X denote the absolute value of the difference of the two numbers. Find the probability distribution of X. Give the probabilities as decimals rounded to three decimal places. B) C) D) A) x P(X = x) x P(X = x) x P(X = x) x P(X = x) 1 0.278 0 0.167 0 0.167 0 0.167 2 0.222 1 0.167 1 0.251 1 0.278 3 0.167 2 0.167 2 0.222 2 0.222 4 0.111 3 0.167 3 0.167 3 0.167 5 0.056 4 0.167 4 0.111 4 0.111 5 0.167 5 0.056 5 0.056 6 0.027 314) When two balanced dice are rolled, 36 equally likely outcomes are possible as shown below. (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6) (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6) (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6) (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6) (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6) Let X denote the smaller of the two numbers. If both dice come up the same number, then X equals that common value. Find the probability distribution of X. Leave your probabilities in fraction form. B) C) D) A) x P(X = x) x P(X = x) x P(X = x) x P(X = x) 1 5/18 1 1/6 1 5/18 1 11/36 2 2/9 2 1/6 2 1/4 2 1/4 3 1/6 3 1/6 3 7/36 3 7/36 4 1/9 4 1/6 4 5/36 4 5/36 5 1/18 5 1/6 5 1/9 5 1/12 6 0 6 1/6 6 1/36 6 1/36 79 314) 315) When two balanced dice are rolled, 36 equally likely outcomes are possible as shown below. (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6) (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6) (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6) (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6) (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6) Let X denote the product of the two numbers. Find the probability distribution of X. Leave your probabilities in fraction form. B) A) x P(X = x) x P(X = x) x P(X = x) x P(X = x) 10 1/12 1/9 1 1/36 12 2 1/18 12 1/9 1/18 2 1/18 15 3 1/18 15 1/12 1/36 3 1/18 16 4 1/12 18 1/12 1/18 4 1/12 18 5 1/18 20 1/12 1/18 5 1/18 20 6 1/9 24 1/12 1/18 6 1/9 24 8 1/18 30 1/18 1/36 8 1/18 25 1/18 9 1/36 30 1/36 10 1/18 36 C) D) x P(X = x) x P(X = x) x P(X = x) x P(X = x) 7 1/6 1/18 1 1/18 12 2 1/36 8 5/36 1/18 2 1/18 15 3 1/18 9 1/9 1/18 3 1/18 16 4 1/12 10 1/12 1/18 4 1/18 18 5 1/9 11 1/18 1/18 5 1/18 20 6 5/36 12 1/36 1/18 6 1/18 24 1/18 8 1/18 25 1/18 9 1/18 30 1/18 10 1/18 36 80 315) 316) The following table displays a frequency distribution for the number of living grandparents for students at a high school. For a randomly selected student in the school, let X denote the number of living grandparents of the student. Obtain the probability distribution of X. 316) Number of living grandparents 0 1 2 3 4 Frequency 37 83 151 206 140 A) B) Grandparents Probability Grandparents Probability x P(X = x) x P(X = x) 0 0.2 1 0.143 1 0.2 2 0.260 2 0.2 3 0.355 3 0.2 4 0.241 4 0.2 C) D) Grandparents Probability Grandparents Probability x P(X = x) x P(X = x) 0 0.060 0 0.068 1 0.135 1 0.151 2 0.245 2 0.245 3 0.334 3 0.318 4 0.227 4 0.219 317) The following table displays a frequency distribution for the number of siblings for students at one middle school. For a randomly selected student in the school, let X denote the number of siblings of the student. Obtain the probability distribution of X. Number of siblings 0 1 2 3 4 5 6 7 Frequency 199 243 126 59 23 8 6 2 A) Siblings Probability x P(X = x) 1 0.520 2 0.270 3 0.126 4 0.049 5 0.017 6 0.013 7 0.004 B) Siblings Probability x P(X = x) 0 0.314 1 0.350 2 0.201 3 0.077 4 0.035 5 0.012 6 0.009 7 0.003 C) D) Siblings Probability x P(X = x) 0 0.125 1 0.125 2 0.125 3 0.125 4 0.125 5 0.125 6 0.125 7 0.125 Siblings Probability x P(X = x) 0 0.299 1 0.365 2 0.189 3 0.089 4 0.035 5 0.012 6 0.009 7 0.003 81 317) 318) The following frequency table contains data on home sale prices in the city of Summerhill for the month of June. For a randomly selected sale price between $80,000 and $265,900 let X denote the number of homes that sold for that price. Find the probability distribution of X. Sale Price (in thousands) 80.0 - 110.9 111.0 - 141.9 142.0 - 172.9 173.0 - 203.9 204.0 - 234.9 235.0 - 265.9 Frequency (No. of homes sold) 2 5 7 10 3 1 A) B) Sale Price (in thousands) Probability (P(X = x) 80.0 - 110.9 0.071 111.0 - 141.9 0.197 142.0 - 172.9 0.250 173.0 - 203.9 0.357 204.0 - 234.9 0.107 235.0 - 265.9 0.036 Sale Price (in thousands) Probability (P(X = x) 80.0 - 110.9 0.071 111.0 - 141.9 0.179 142.0 - 172.9 0.250 173.0 - 203.9 0.357 204.0 - 234.9 0.107 235.0 - 265.9 0.360 C) D) Sale Price (in thousands) Probability (P(X = x) 80.0 - 110.9 0.071 111.0 - 141.9 0.179 142.0 - 172.9 0.250 173.0 - 203.9 0.357 204.0 - 234.9 0.107 235.0 - 265.9 0.036 Sale Price (in thousands) Probability (P(X = x) 80.0 - 110.9 0.071 111.0 - 141.9 0.179 142.0 - 172.9 0.025 173.0 - 203.9 0.357 204.0 - 234.9 0.107 235.0 - 265.9 0.036 82 318) Construct the requested histogram. 319) If a fair coin is tossed 4 times, there are 16 possible sequences of heads (H) and tails (T). Suppose the random variable X represents the number of heads in a sequence. Construct the probability distribution for X. A) B) C) D) 83 319) 320) Each person from a group of recently graduated math majors revealed the number of job offers that he or she had received prior to graduation. The compiled data are represented in the table. Construct the probability histogram for the number of job offers received by a graduate randomly selected from this group. 320) Number of offers 0 1 2 3 4 Frequency 4 10 25 5 6 A) B) C) D) Find the specified probability. 321) A statistics professor has office hours from 9:00 am to 10:00 am each day. The number of students waiting to see the professor is a random variable, X, with the distribution shown in the table. 321) x 0 1 2 3 4 5 P(X = x) 0.05 0.10 0.40 0.25 0.15 0.05 The professor gives each student 10 minutes. Determine the probability that a student arriving just after 9:00 am will have to wait no longer than 20 minutes to see the professor. A) 0.80 B) 0.55 C) 0.40 D) 0.15 322) A statistics professor has office hours from 9:00 am to 10:00 am each day. The number of students waiting to see the professor is a random variable, X, with the distribution shown in the table. x 0 1 2 3 4 5 P(X = x) 0.05 0.10 0.40 0.25 0.15 0.05 The professor gives each student 10 minutes. Determine the probability that a student arriving just after 9:00 am will have to wait at least 30 minutes to see the professor. A) 0.45 B) 0.25 C) 0.15 D) 0.85 84 322) 323) The number of loaves of rye bread left on the shelf of a local bakery at closing (denoted by the random variable X) varies from day to day. Past records show that the probability distribution of X is as shown in the following table. Find the probability that there will be at least three loaves left over at the end of any given day. x 0 1 2 3 4 5 6 P(X = x) 0.20 0.25 0.20 0.15 0.10 0.08 0.02 A) 0.20 B) 0.15 C) 0.65 D) 0.35 323) 324) There are only 8 chairs in our whole house. Whenever there is a party some people have no where to sit. The number of people at our parties (call it the random variable X) changes with each party. Past records show that the probability distribution of X is as shown in the following table. Find the probability that everyone will have a place to sit at our next party. x 5 6 7 8 9 10 >10 P(X = x) 0.05 0.05 0.20 0.15 0.15 0.10 0.30 A) 0.55 B) 0.15 C) 0.05 D) 0.45 324) 325) Use the special addition rule and the following probability distribution to determine P(X ≥ 8). x 5 6 7 8 9 10 11 P(X = x) 0.05 0.05 0.20 0.15 0.15 0.10 0.30 A) 0.30 B) 0.15 C) 0.45 D) 0.70 325) 326) Use the special addition rule and the following probability distribution to determine P(X = 6). x 5 6 7 8 9 10 11 P(X = x) 0.05 0.05 0.20 0.15 0.15 0.10 0.30 A) 0.10 B) 0.95 C) 0.05 D) 0.90 326) 327) Use the special addition rule and the following probability distribution to determine P(6 < X ≤ 8). x 5 6 7 8 9 10 11 P(X = x) 0.05 0.05 0.20 0.15 0.15 0.10 0.30 A) 1.00 B) 0.45 C) 0.35 D) 0.40 327) Calculate the specified probability 328) Suppose that W is a random variable. Given that P(W ≤ 3) = 0.425, find P(W > 3). A) 0.425 B) 3 C) 0 D) 0.575 328) 329) Suppose that D is a random variable. Given that P(D > 1.8) = 0.65, find P(D ≤ 1.8). A) 0 B) 0.35 C) 0.65 D) 0.175 329) 330) Suppose that K is a random variable. Given that P(-3.65 ≤ K ≤ 3.65) = 0.125, and that P(K < -3.65) = P(K > 3.65), find P(K > 3.65). A) 0.4375 B) 0.125 C) 0.875 D) 1.825 330) 331) Suppose that T is a random variable. Given that P(2.55 ≤ T ≤ 2.55) = 0.8, and that P(K < 2.55) = P(K > 2.55), find P(K < -2.55). A) 0.1 B) 0.8 C) 1.275 D) 0.2 331) 332) Suppose that A is a random variable. Also suppose that P(T > a) = P(T < -a) = x, and that P(0 < T ≤ a ) = y. Find P(-a ≤ T ≤ 0) in terms of x and y. A) 1 - y B) y C) 1 - (2x - y) D) 1 - 2x - y 332) 85 Find the mean of the random variable. 333) The random variable X is the number of houses sold by a realtor in a single month at the Sendsomʹs Real Estate office. Its probability distribution is given in the table. x P(X = x) 0 0.24 1 0.01 2 0.12 3 0.16 4 0.01 5 0.14 6 0.11 7 0.21 A) 3.35 B) 3.50 C) 3.40 D) 3.60 333) 334) The random variable X is the number of golf balls ordered by customers at a pro shop. Its probability distribution is given in the table. x 3 6 9 12 15 P(X = x) 0.14 0.33 0.36 0.07 0.10 A) 9 B) 9.54 C) 7.98 D) 5.31 334) 335) The random variable X is the number of people who have a college degree in a randomly selected group of four adults from a particular town. Its probability distribution is given in the table. x P(X = x) 0 0.4096 1 0.4096 2 0.1536 3 0.0256 4 0.0016 A) 2.00 B) 1.21 C) 0.80 D) 0.70 335) 336) The random variable X is the number that shows up when a loaded die is rolled. Its probability distribution is given in the table. x P(X = x) 1 0.11 2 0.11 3 0.11 4 0.12 5 0.13 6 0.42 A) 3.50 B) 4.18 C) 4.31 D) 0.17 336) 337) The random variable X is the number of siblings of a student selected at random from a particular secondary school. Its probability distribution is given in the table. 337) x 0 1 2 3 4 5 1 1 13 7 1 7 P(X = x) 48 24 6 48 12 24 A) 1.5 B) 1.875 C) 1.604 86 D) 2.5 Find the standard deviation of the random variable. 338) A police department reports that the probabilities that 0, 1, 2, and 3 burglaries will be reported in a given day are 0.51, 0.36, 0.11, and 0.02, respectively. Find the standard deviation for the probability distribution. A) 1.04 B) 0.76 C) 0.99 D) 0.57 338) 339) The random variable X is the number of houses sold by a realtor in a single month at the Sendsomʹs Real Estate office. Its probability distribution is given in the table. Houses Sold (x) Probability P(x) 0 0.24 1 0.01 2 0.12 3 0.16 4 0.01 5 0.14 6 0.11 7 0.21 A) 4.45 B) 2.62 C) 2.25 D) 6.86 339) 340) The random variable X is the number of people who have a college degree in a randomly selected group of four adults from a particular town. Its probability distribution is given in the table. x P(X = x) 0 0.0256 1 0.1536 2 0.3456 3 0.3456 4 0.1296 A) 2.59 B) 0.96 C) 0.98 D) 1.12 340) 341) The probabilities that a batch of 4 computers will contain 0, 1, 2, 3, and 4 defective computers are 0.5997, 0.3271, 0.0669, 0.0061, and 0.0002, respectively. A) 0.59 B) 0.65 C) 0.42 D) 0.81 341) 342) A police department reports that the probabilities that 0, 1, 2, and 3 burglaries will be reported in a given day are 0.51, 0.40, 0.07, and 0.02, respectively. Find the standard deviation for the probability distribution. A) 0.50 B) 0.71 C) 0.93 D) 1.00 342) 343) The random variable X is the number of siblings of a student selected at random from a particular secondary school. Its probability distribution is given in the table. 343) x 0 1 2 3 4 5 5 1 1 1 13 5 P(X = x) 48 16 24 8 24 24 A) 1.606 B) 0.964 C) 1.927 D) 1.338 The probability distribution of a random variable is given along with its mean and standard deviation. Draw a probability histogram for the random variable; locate the mean and show one, two, and three standard deviation intervals. 87 344) x 4 5 6 7 8 P(X = x) 0.1 0.3 0.45 0.1 0.05 344) μ = 5.7, σ = 0.95 A) B) C) 345) The random variable X is the number of tails when four coins are flipped. Its probability distribution is as follows. x 0 1 2 3 4 1 1 3 1 1 P(X = x) 16 4 8 4 16 μ = 2, σ = 1 88 345) A) B) C) Find the expected value of the random variable. 346) Suppose you buy 1 ticket for $1 out of a lottery of 1,000 tickets where the prize for the one winning ticket is to be $500. What is your expected value? A) -$1.00 B) -$0.40 C) $0.00 D) -$0.50 347) In a game, you have a 1/26 probability of winning $57 and a 25/26 probability of losing $4. What is your expected value? A) -$3.85 B) $2.19 C) $6.04 D) -$1.65 89 346) 347) 348) A contractor is considering a sale that promises a profit of $27,000 with a probability of 0.7 or a loss (due to bad weather, strikes, and such) of $17,000 with a probability of 0.3. What is the expected profit? A) $30,800 B) $18,900 C) $13,800 D) $10,000 348) 349) Suppose you pay $2.00 to roll a fair die with the understanding that you will get back $ 4.00 for rolling a 2 or a 3, nothing otherwise. What is your expected value? A) $2.00 B) -$0.67 C) $4.00 D) -$2.00 349) 350) Suppose you buy 1 ticket for $1 out of a lottery of 1,000 tickets where the prize for the one winning ticket is to be $500. What is your expected value? A) -$0.50 B) -$1.00 C) $0.00 D) -$0.40 350) 351) Sue Anne owns a medium-sized business. Use the probability distribution below, where X describes the number of employees who call in sick on a given day. 351) Number of Employees Sick 0 1 2 3 4 P(X = x) 0.05 0.45 0.25 0.15 0.1 What is the expected value of the number of employees calling in sick on any given day? A) 1.85 B) 2.00 C) 1.80 D) 1.00 352) The probability distribution below describes the number of thunderstorms that a certain town may experience during the month of August. Let X represent the number of thunderstorms in August. Number of storms 0 1 2 3 P(X = x) 0.1 0.3 0.5 0.1 What is the expected value of thunderstorms for the town each August? A) 1.5 B) 2.0 C) 1.6 90 D) 1.7 352)