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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)