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test 4 review 1010 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find the area under the normal curve for the condition. 7) Find the percent of the area under the curve between the mean and 3.01 standard deviations from the mean. Use the given data to construct a frequency and relative frequency distribution. 1) Kevin asked some of his friends how many hours they had worked during the previous week at their after-school jobs. The results are shown below. 6 5 5 6 4 8 6 5 6 6 8 6 9 5 Use the standard normal curve table to find the closest z-score for the given condition. 8) 74.9% of the total area is to the left of z. A company installs 5,000 light bulbs. The lifetimes of the lightbulbs are approximately normally distributed with a mean of 500 hours and a standard deviation of 100 hours. Find the approximate number of bulbs that can be expected to last the indicated amount of time. 9) More than 740 hours 8 6 4 8 5 8 5 8 8 4 Construct a frequency and relative frequency distribution. Use 4 classes. Find the mean of the set of data. 2) 3.5 1.6 2.4 3.7 4.1 3.9 1.0 3.6 4.2 3.4 3.7 2.2 1.5 4.2 3.4 2.7 0.4 3.7 2.0 3.6 Find the indicated probability or percentage for the normally distributed variable. 10) A machine produces pencils with a mean diameter of 0.30 inches and a standard deviation of 0.01 inches. The diameters are approximately normally distributed. What is the probability that a randomly selected pencil has a diameter less than 0.285 inches? Round your answer to two decimal places. Find the range for the set of data given. 3) 117 527 136 607 404 Solve the problem. 11) Scores on a test are approximately normally distributed with a mean of 70 and a standard deviation of 9. The teacher wants to give A's to the top 10% of students, B's to the next 25%, and C's to the next 42%. What is the bottom cutoff for a C grade? Round your answer to the nearest whole number. 237 Solve the problem. 4) At Loop Junior College, the mean grade point average (gpa) of the current student body is 2.76 with a standard deviation of 0.64. Compute the gpa's of each student to two decimal places. 12) At Loop College, the mean grade point average (gpa) of the current student body is 2.76 with a standard deviation of 0.64. Find the gpa of a student whose z-score is -2.8. Round A gpa with a z-score of 0.6. A gpa with a z-score of -1.2. Classify the random variable as either discrete or continuous. 5) The number of colleges in a state to the nearest hundredth. Rank the data from lowest to highest and determine the requested quartile. 13) The following scores on the midterm exam in Chemistry 102 were recorded. At one high school, the mean time for running the 100-yard dash is 15.2 seconds with a standard deviation of 0.9 seconds. The times are very closely approximated by a normal curve. Find the percent of times that are: 6) Between 15.2 and 16.1 seconds 93 81 59 69 82 74 61 77 95 84 88 71 85 97 63 72 89 80 60 98 91 62 78 83 76 81 94 66 83 96 Find the 1st quartile, Q1 . 1 Find the indicated decile or percentile. 14) The test scores of 19 students are listed below. Find the sixth decile, D6 . 36 56 68 88 45 59 70 91 49 61 74 92 Provide an appropriate response. 20) We want to compare two different groups of students, students taking Composition 1 in a traditional lecture format and students taking Composition 1 in a distance learning format. We know that the mean score on the research paper is 85 for both groups. What additional information would be provided by knowing the standard deviation? 53 55 62 65 78 84 99 Solve. Find the median. 21) 31, 14, 7, 5, 24, 12, 29, 31, 40, 35 15) Find the mode or modes. 22) 7.07, 7.41, 7.56, 7.07, 7.88, 7.99, 7.62 Give the median of the data set represented by the box plot above. Find the mean for the given frequency distribution. 23) Value Frequency 12 2 17 12 22 20 31 13 33 10 True or false? 16) A person who scored at the eightieth percentile in a test answered eighty percent of the questions correctly. Find the standard deviation. Round to one more place than the data. 17) 2, 3, 16, 18, 6, 19, 11, 18, 17 Find the median for the given frequency distribution. Value Frequency 60 4 62 8 24) 64 12 66 20 68 31 70 13 Use Chebyshev's theorem to solve the problem. 18) In a certain distribution of numbers, the mean is 50 and the standard deviation is 6. What can you say about the percentage of numbers that lie between 29 and 71? 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. 25) Last year, nine employees of an electronics company retired. Their ages at retirement are listed below. Find the mean retirement age. Find the standard deviation for the given data. Round your final answer to one more decimal place than that used for the observations. 19) Christine is currently taking college astronomy. The instructor often gives quizzes. On the past seven quizzes, Christine got the following scores. 51 20 114 25 10 46 56 67 55 68 61 50 58 2 63 58 54 Find the median for the given sample data. 26) The weights (in ounces) of 21 cookies are shown. Find the median weight. Construct a frequency polygon. 30) Number of Number of vacation days employees 1-5 10 6-10 25 11-15 35 16-20 20 21-25 10 0.72 1.26 0.80 1.62 0.86 0.60 1.09 1.26 1.53 0.95 0.72 1.45 1.03 0.80 0.47 1.45 0.60 1.03 1.72 0.86 0.56 Solve the problem. 27) Jackie's sisters weigh 117 lb, 148 lb, 128 lb, and 125 lb. The average female in her city weighs 139.1 lb. How much does Jackie weigh if she and her sisters have an average weight of 139.1 lb? Provide an appropriate response. 28) The median of a data set is always/sometimes/never (select one) one of the data points in a set of data. Explain your answer with brief examples. Construct a stem and leaf display for given data. 31) Mr. Johnson wants to display his employees' ages in a graph. Below are their ages. 23 36 45 42 34 53 34 27 24 Construct the specified histogram. 29) The ages of the voters at a poll during a 20-minute period are listed below. Use five classes with a uniform width of 10 years, where the lower limit of the first class is 20 years. Use this graph to answer the question. Big "D" Sales for 2009, 2010 35 29 48 63 64 38 21 23 41 68 61 42 43 47 33 37 46 27 23 30 Sales (thousands of dollars) 2010 2009 Month 32) What month in 2010 had the lowest sales? 3 Answer the question. 33) The bar graph below shows the number of students by major in the College of Arts and Sciences. In a school survey, students showed these preferences for instructional materials. Answer the question. 35) How many degrees are in the central angle for the "Lecture" sector? MAJOR Use the information to complete a circle graph. Note that the circle is divided into 100 equal sections. 36) Main form of exercise for employees of one company: None: 30% Walking: 18% Running: 4% Golf: 11% Weight Training: 26% Other: 11% Did twice as many students major in English as in Math? This double-bar graph shows the number of male (M) and female (F) athletes at a university over a four-year period. Answer the question. YEAR 34) Which year had the smallest number of female athletes? 4 Use the graph to answer the question. 37) Make a bar graph to represent the data. 40) Construct a vertical 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 Mike decides to buy shares of companies A, B, and C, which were initially selling for the same price. The changes in each stock's value are shown in the graph above. At its peak, stock A was valued at approximately how much more than either B or C? Provide an appropriate response. 41) Shortly before a mayoral election, a market research firm took a poll to find out which candidate people were planning to vote for. The results are shown below. Solve the problem. 38) Sixteen workers were surveyed about how long it takes them to travel to work each day. The data below are given in minutes. Represent the data in a double-stem display. 20 35 42 20 24 37 23 24 22 20 41 25 28 27 30 32 Candidate Li Fong Bob Green Sue Moore Jose Alvarez Find the indicated probability. 39) A relative frequency distribution is given below for the size of families in one U.S. city. Size 2 3 4 5 6 7+ Frequency 2120 2329 1042 399 You wish to construct a graph to represent the data. It should be easy to see from your graph which candidate is in the lead. Which graph would be more useful, a bar graph or a pie chart? Explain your thinking. Relative frequency 0.448 0.208 0.203 0.094 0.029 0.018 A family is selected at random. Find the probability that the size of the family is between 2 and 5 inclusive. Round your answer to three decimal places. 5 Answer Key Testname: UNTITLED1 1) Hours Frequency Relative Frequency x f f/n 3-4 3 3/24 ≈ 13% 5-6 13 13/24 ≈ 54% 7- 8 7 7/24 ≈ 29% 9-10 1 1/24 ≈ 4% 2) 2.94 3) 490 4) 3.14, 1.99 5) Discrete 6) 34% 7) 49.9% 8) 0.67 9) 40 10) 0.067 11) 63 12) 0.97 13) 71 14) 70 15) 35 16) False 17) 6.9 18) at least 91.8% 19) 34.7 20) Answers will vary. Possible answer: The standard deviation will give an indication of how widely the scores vary. More precisely, it gives an indication of how much the scores deviate, on average, from the mean score of 85. 21) 26.5 22) 7.07 23) 24.6 24) 67 25) 59.1 26) 0.95 ounces 27) 177.5 lb 28) Answers will vary. Possible answer: The median is sometimes one of the data points. If the number of data points is odd, the median will be one of the data points (the middle data point). If the number of data points is even, the median is the average of the two middle data points which will be equal to one of the data points only if the two middle data points are identical. 6 Answer Key Testname: UNTITLED1 29) 30) Frequency Number of vacation days 31) 2 347 3 446 4 25 53 32) Month 2 33) Yes 34) 1986 35) 64.8° 36) 37) $35 38) (20-24) (25-29) (30-34) (35-39) (40-44) 39) 0.953 2 2 3 3 4 0002344 578 02 57 12 7 Answer Key Testname: UNTITLED1 40) 41) Answers will vary. Possible answer: A bar graph would be more useful. A bar graph is useful for comparing the sizes of different categories with each other, since it is easy to compare the heights of different bars. 8