Pathway to Introductory Statistics 1st Edition Lehmann – Test Bank

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Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Express the indicated degree of likelihood as a probability value.
1) “You have a 50-50 chance of choosing the correct answer.”
A) 0.50 B) 50 C) 0.9 D) 0.25
1)
2) “There is a 40% chance of rain tomorrow.”
A) 0.40 B) 4 C) 0.60 D) 40
2)
3) “You cannot determine the exact decimal-number value of π.”
A) 0 B) 0.5 C) 3.14 D) 1
3)
4) “Your mother could not have died two years before you were born.”
A) 0.5 B) 0 C) 0.25 D) 1
4)
5) “It will definitely turn dark tonight.”
A) 0.30 B) 1 C) 0.5 D) 0.67
5)
6) “You have one chance in ten of winning the race.”
A) 0.10 B) 0.90 C) 1 D) 0.5
6)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
7) (a) Simulate the experiment of sampling 100 four-child families to estimate the probability
that a four-child family has three girls. Assume that the outcomes “have a girl” and “have a boy”
are equally likely.
(b) Simulate the experiment of sampling 1000 four-child families to estimate the probability
that a four-child family has three girls. Assume that the outcomes “have a girl” and “have a boy”
are equally likely.
The classical probability that a four-child family has three girls is 1
4 .
Compare the results of (a) and (b) to the probability that would be obtained using the classical
method.
Which answer was closer to the probability that would be obtained using the classical method? Is
this what you would expect?
7)
1
8) (a) Use a graphing calculator or statistical software to simulate drawing a card from a standard
deck 100 times (with replacement of the card after each draw). Use an integer distribution with
numbers 1 through 4 and use the results of the simulation to estimate the probability of getting a
spade when a card is drawn from a standard deck.
(b) Simulate drawing a card from a standard deck 400 times (with replacement of the card after
each draw). Estimate the probability of getting a spade when a card is drawn from a standard
deck.
Compare the results of (a) and (b) to the probability that would be obtained using the classical
method.
Which simulation resulted in the closest estimate to the probability that would be obtained using
the classical method? Is this what you would expect?
8)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the indicated probability.
9) A sample space consists of 197 separate events that are equally likely. What is the probability of
each?
A) 197 B) 1
197 C) 0 D) 1
9)
10) 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?
A) 1 B) 0 C) 1
7 D) 7
10)
11) A die with 12 sides is rolled. What is the probability of rolling a number less than 11?
A) 11
12 B) 5
6 C) 1
12 D) 10
11)
12) A bag contains 2 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?
A) 1
7 B) 1
4 C) 1
9 D) 1
3
12)
13) Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice
will be 5?
A) 5
6 B) 8
9 C) 1
9 D) 4
13)
14) If a person is randomly selected, find the probability that his or her birthday is in May. Ignore leap
years.
A) 1
31 B) 1
365 C) 1
12 D) 31
365
14)
15) A class consists of 50 women and 21 men. If a student is randomly selected, what is the probability
that the student is a woman?
A) 50
21 B) 50
71 C) 21
71 D) 1
71
15)
2
Provide an appropriate response.
16) A question has five multiple-choice answers. Find the probability of guessing an incorrect answer.
A) 3
5 B) 4
5 C) 5
2 D) 1
5
16)
17) A question has five multiple-choice questions. Find the probability of guessing the correct answer.
A) 4
5 B) 2
5 C) 5
4 D) 1
5
17)
18) A single die is rolled twice. The set of 36 equally likely outcomes is {(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)}. Find the
probability of getting two numbers whose sum is greater than 9.
A) 1
4 B) 1
12 C) 1
6 D) 6
18)
19) A single die is rolled twice. The set of 36 equally likely outcomes is {(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)}. Find the
probability of getting two numbers whose sum is less than 13.
A) 1
2 B) 0 C) 1
4 D) 1
19)
20) A single die is rolled twice. The set of 36 equally likely outcomes is {(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)}. Find the
probability of getting two numbers whose sum is greater than 9 and less than 13.
A) 0 B) 7
36 C) 5
36 D) 1
6
20)
Answer the question.
21) Which of the following cannot be a probability?
A) -1 B) 0 C) 1
2 D) 1
21)
22) Which of the following cannot be a probability?
A) 5
3 B) 1
2 C) 2
3 D) 3
5
22)
23) What is the probability of an event that is certain to occur?
A) 0.99 B) 1 C) 0.5 D) 0.95
23)
24) What is the probability of an impossible event?
A) 0 B) -1 C) 0.1 D) 1
24)
3
25) On a multiple choice test with four possible answers for each question, what is the probability of
answering a question correctly if you make a random guess?
A) 1 B) 3
4 C) 1
4 D) 1
2
25)
Provide an appropriate response.
26) Use the spinner below to answer the question. Assume that it is equally probable that the pointer will land
on any one of the five numbered spaces. If the pointer lands on a borderline, spin again.
Find the probability that the arrow will land on 2 or 3.
A) 3
2 B) 1 C) 2 D) 2
5
26)
27) Use the spinner below to answer the question. Assume that it is equally probable that the pointer will land
on any one of the five numbered spaces. If the pointer lands on a borderline, spin again.
Find the probability that the arrow will land on an odd number.
A) 2
5 B) 1 C) 3
5 D) 0
27)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
28) Use the pie chart, which shows the number of Congressional Medal of Honor recipients in the
United States, to find the probability that a randomly chosen recipient served in the Navy.
28)
4
29) Use the pie chart, which shows the number of Congressional Medal of Honor recipients in the
United States, to find the probability that a randomly chosen recipient did not serve in the
Marines.
29)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use the empirical rule to solve the problem.
30) The systolic blood pressure of 18-year-old women is normally distributed with a mean of 120
mmHg and a standard deviation of 12 mmHg. What is the probability than an 18-year-old women
will have a systolic blood pressure between 96 mmHg and 144 mmHg?
A) 0.997 B) 0.95 C) 0.68
30)
Solve the problem.
31) A probability experiment is conducted in which the sample space of the experiment is
S = {5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}. Let event A = {8, 9, 10, 11, 12}. Assume that each outcome is
equally likely. List the outcomes in Ac. Find P(Ac).
A) {5, 6, 7, 12, 13, 14, 15}; 7
11 B) {8, 9, 10, 11, 12}; 5
11
C) {13, 14, 15}; 3
11 D) {5, 6, 7, 13, 14, 15}; 6
11
31)
32) You are dealt one card from a 52-card deck. Find the probability that you are not dealt a 10.
Express the probability as a simplified fraction.
A) 12
13 B) 1
13 C) 1
10 D) 9
10
32)
33) You are dealt one card from a 52-card deck. Find the probability that you are not dealt a spade.
Express the probability as a simplified fraction.
A) 4
13 B) 3
4 C) 1
4 D) 2
5
33)
5
34) In 5-card poker, played with a standard 52-card deck, 2,598,960 different hands are possible. If
there are 624 different ways a “four-of-a-kind” can be dealt, find the probability of not being dealt
a “four-of-a-kind”. Express the probability as a fraction, but do not simplify.
A) 625
2,598,960 B) 624
2,598,960 C) 2,598,336
2,598,960 D) 1248
2,598,960
34)
35) A certain disease only affects men 20 years of age or older. The chart shows the probability that a man
with the disease falls in the given age group. What is the probability that a randomly selected man with the
disease is not between the ages of 55 and 64?
Age Group Probability
20-24 0.004
25-34 0.006
35-44 0.14
45-54 0.29
55-64 0.32
65-74 0.17
75+ 0.07
A) 0.29 B) 0.24 C) 0.32 D) 0.68
35)
36) A certain disease only affects men 20 years of age or older. The chart shows the probability that a man
with the disease falls in the given age group. What is the probability that a randomly selected man with the
disease is between the ages of 35 and 64?
Age Group Probability
20-24 0.004
25-34 0.006
35-44 0.14
45-54 0.29
55-64 0.32
65-74 0.17
75+ 0.07
A) 0.75 B) 0.32 C) 0.14 D) 0.29
36)
37) The overnight shipping business has skyrocketed in the last ten years. The single greatest predictor
of a company’s success has been proven time and again to be customer service. A study was
conducted to study the customer satisfaction levels for one overnight shipping business. In addition
to the customer’s satisfaction level, the customers were asked how often they used overnight
shipping. The results are shown below in the following table. What is the probability that a
respondent did not have a medium level of satisfaction with the company? Round the the nearest
hundredth.
Frequency of Use High
Satisfaction level
Medium Low TOTAL
< 2 per month 250 140 10 400
2 – 5 per month 140 55 5 200
> 5 per month 70 25 5 100
TOTAL 460 220 20 700
A) 0.31 B) 0.29 C) 0.69 D) 0.71
37)
6
38) A sample of 255 shoppers at a large suburban mall were asked two questions: (1) Did you see a
television ad for the sale at department store X during the past 2 weeks? (2) Did you shop at
department store X during the past 2 weeks? The responses to the questions are summarized in the
table. What is the probability that a randomly selected shopper from the 255 questioned did not shop
at department store X? Round the the nearest thousandth.
Shopped at X Did Not Shop at X
Saw ad 135 25
Did not see ad 25 70
A) 0.627 B) 0.275 C) 0.373 D) 0.098
38)
39) After completing an inventory of three warehouses, a golf club shaft manufacturer described its
stock of 12,246 shafts with the percentages given in the table. Suppose a shaft is selected at random
from the 12,246 currently in stock, and the warehouse number and type of shaft are observed. Find
the probability that the shaft was produced in a warehouse other than warehouse 1. Round the the
nearest hundredth.
Type of Shaft
Regular Stiff Extra Stiff
1 19% 8% 17%
Warehouse 2 14% 7% 7%
3 10% 18% 0%
A) 0.44 B) 0.76 C) 0.43 D) 0.56
39)
40) The breakdown of workers in a particular state according to their political affiliation and type of job held is
shown here. Suppose a worker is selected at random within the state and the worker’s political affiliation
and type of job are noted. Find the probability the worker is not an Independent. Round the the nearest
hundredth.
Political Affiliation
Republican Democrat Independent
White collar 7% 16% 9%
Type of job
Blue Collar 14% 18% 36%
A) 0.23 B) 0.32 C) 0.45 D) 0.55
40)
41) A probability experiment is conducted in which the sample space of the experiment is
S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}. Let event A = {3, 4, 5, 6} and event B = {11, 12, 13}.
Assume that each outcome is equally likely. List the outcomes in A and B. Are A and B mutually
exclusive?
A) {3, 4, 5, 6, 11, 12, 13}; yes B) { }; no
C) {3, 4, 5, 6, 11, 12, 13}; no D) { }; yes
41)
42) The events A and B are mutually exclusive. If P(A) = 0.2 and P(B) = 0.3, what is P(A or B)?
A) 0.06 B) 0 C) 0.5 D) 0.1
42)
43) The table lists the drinking habits of a group of college students. If a student is chosen at random, find the
probability of getting someone who is a regular or heavy drinker. Round your answer to three decimal
places.
Sex Non-drinker Regular Drinker Heavy Drinker Total
Man 135 44 5 184
Woman 187 21 6 214
Total 322 65 11 398
A) 0.191 B) 0.126 C) 0.218 D) 0.658
43)
7
44) The table lists the drinking habits of a group of college students. If a student is chosen at random, find the
probability of getting someone who is a man or a woman. Round your answer to three decimal places.
Sex Non-drinker Regular Drinker Heavy Drinker Total
Man 135 69 5 209
Woman 187 21 12 220
Total 322 90 17 429
A) 0.249 B) 1 C) 0.751 D) 0.923
44)
45) The table lists the drinking habits of a group of college students. If a student is chosen at random,
find the probability of getting someone who is a non-drinker. Round your answer to three decimal
places.
Sex Non-drinker Regular Drinker Heavy Drinker Total
Man 135 49 5 189
Woman 187 21 6 214
Total 322 70 11 403
A) 0.799 B) 1 C) 0.201 D) 0.933
45)
46) The distribution of Bachelor’s degrees conferred by a university is listed in the table. Assume that a student
majors in only one subject. What is the probability that a randomly selected student with a Bachelor’s
degree majored in Physics or Philosophy? Round your answer to three decimal places.
Major Frequency
Physics 226
Philosophy 208
Engineering 86
Business 176
Chemistry 222
A) 0.246 B) 0.473 C) 0.527 D) 0.227
46)
47) The distribution of Bachelor’s degrees conferred by a university is listed in the table. Assume that a student
majors in only one subject. What is the probability that a randomly selected student with a Bachelor’s
degree majored in Business, Chemistry or Engineering? Round your answer to three decimal places.
Major Frequency
Physics 216
Philosophy 207
Engineering 89
Business 170
Chemistry 215
A) 0.289 B) 0.528 C) 0.472 D) 0.339
47)
48) A probability experiment is conducted in which the sample space of the experiment is
S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}. Let event A = {8, 9, 10, 11} and event
B = {10, 11, 12, 13, 14}. Assume that each outcome is equally likely. List the outcomes in A or B.
Find P(A or B).
A) {8, 9, 10, 11, 12, 12, 13, 14}; 3
5 B) {10, 11}; 2
15
C) {8, 9, 10, 11, 12, 13, 14}; 7
15 D) {8, 9, 10, 11, 13, 14}; 2
5
48)
49) The events A and B are mutually exclusive. If P(A) = 0.1 and P(B) = 0.5, what is P(A and B)?
A) 0.05 B) 0.6 C) 0.5 D) 0
49)
8
50) Given that P(A or B) = 1
2 , P(A) = 1
7 , and P(A and B) = 1
8 , find P(B). Express the probability as a
simplified fraction.
A) 43
56 B) 27
56 C) 29
56 D) 17
112
50)
51) The table lists the drinking habits of a group of college students. If a student is chosen at random,
find the probability of getting someone who is a man or a non-drinker. Round your answer to three
decimal places.
Sex Non-drinker Regular Drinker Heavy Drinker Total
Man 135 52 5 192
Woman 187 21 9 217
Total 322 73 14 409
A) 0.927 B) 0.948 C) 0.822 D) 0.941
51)
52) The table lists the drinking habits of a group of college students. If a student is chosen at random, find the
probability of getting someone who is a woman or a heavy drinker. Round your answer to three decimal
places.
Sex Non-drinker Regular Drinker Heavy Drinker Total
Man 135 31 5 171
Woman 187 21 15 223
Total 322 52 20 394
A) 0.117 B) 0.909 C) 0.868 D) 0.579
52)
53) A card is drawn from a standard deck of 52 playing cards. Find the probability that the card is a
queen or a club. Express the probability as a simplified fraction.
A) 2
13 B) 4
13 C) 3
13 D) 7
52
53)
54) One hundred people were asked, “Do you favor stronger laws on gun control?” Of the 33 that
answered “yes” to the question, 14 were male. Of the 67 that answered “no” to the question, six were
male. If one person is selected at random, what is the probability that this person answered “yes” or
was a male? Round the the nearest hundredth.
A) 0.67 B) 0.39 C) 0.53 D) 0.13
54)
55) The below table shows the probabilities generated by rolling one die 50 times and noting the up face.
What is the probability of getting an odd up face and a two or less? Round the the nearest hundredth.
Roll 1 2 3 4 5 6
Probability 0.22 0.10 0.18 0.12 0.18 0.20
A) 0.90 B) 0.66 C) 0.32 D) 0.68
55)
56) You roll two dice and total the up faces. What is the probability of getting a total of 8 or two up
faces that are the same? Round the the nearest hundredth.
A) 0.50 B) 0.28 C) 0.31 D) 0.33
56)
9
57) Consider the data in the table shown which represents the marital status of males and females 18 years or
older in the United States in 2003. Determine the probability that a randomly selected U.S. resident 18
years or older is divorced or a male? Round to the nearest hundredth.
Males
(in millions)
Females
(in millions)
Total
(in millions)
Never married 28.6 23.3 51.9
Married 62.1 62.8 124.9
Widowed 2.7 11.3 14.0
Divorced 9.0 12.7 21.7
Total (in millions) 102.4 110.1 212.5
Source: U.S. Census Bureau, Current Population reports
A) 0.58 B) 0.54 C) 0.04 D) 0.50
57)
58) If one card is drawn from a standard 52 card playing deck, determine the probability of getting a
ten, a king or a diamond. Round to the nearest hundredth.
A) 0.37 B) 0.31 C) 0.40 D) 0.29
58)
59) If one card is drawn from a standard 52 card playing deck, determine the probability of getting a
jack, a three, a club or a diamond. Round to the nearest hundredth.
A) 0.50 B) 0.65 C) 0.58 D) 0.15
59)
60) Two dice are rolled. What is the probability of having both faces the same (doubles) or a total of 4
or 10? Round to the nearest hundredth.
A) 0.33 B) 0.28 C) 0.06 D) 0.15
60)
61) A probability experiment is conducted in which the sample space of the experiment is
S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}. Let event A = {5, 6, 7, 8} and event B = {7, 8, 9, 10, 11}.
Assume that each outcome is equally likely. List the outcomes in A and B. Are A and B mutually
exclusive? Find P(A and B)
A) {7, 8}; no; 2
15 B) {5, 6, 7, 8, 9, 10, 11}; no; 7
15
C) {7, 8}; yes; 2
15 D) {5, 6, 7, 8, 9, 10, 11}; yes; 7
15
61)
62) The complement of 4 heads in the toss of 4 coins is
A) All tails B) Three heads C) At least one tail D) Exactly one tail
62)
63) A local country club has a membership of 600 and operates facilities that include an 18-hole
championship golf course and 12 tennis courts. Before deciding whether to accept new members,
the club president would like to know how many members regularly use each facility. A survey of
the membership indicates that 69% regularly use the golf course, 47% regularly use the tennis
courts, and 3% use neither of these facilities regularly. What percentage of the 600 use at least one
of the golf or tennis facilities?
A) 97% B) 113% C) 19% D) 3%
63)
64) A game has three outcomes. The probability of a win is 0.4, the probability of tie is 0.5, and the
probability of a loss is 0.1. What is the probability of not winning in a single play of the game.
A) 0.6 B) 0.1 C) 0.33 D) 0.5
64)
10
65) In the game of craps two dice are rolled and the up faces are totaled. If the person rolling the dice
on the first roll rolls a 7 or an 11 total they win. If they roll a 2, 3, or 12 on the first roll they lose. If
they roll any other total then on subsequent rolls they must roll that total before rolling a 7 to win.
What is the probability of winning on the first roll?
A) 0.17 B) 0.50 C) 0.06 D) 0.22
65)
Find the indicated probability. Give your answer as a simplified fraction.
66) The overnight shipping business has skyrocketed in the last ten years. The single greatest predictor
of a company’s success has been proven time and again to be customer service. A study was
conducted to study the customer satisfaction levels for one overnight shipping business. In addition
to the customer’s satisfaction level, the customers were asked how often they used overnight
shipping. The results are shown below in the following table. A customer is chosen at random.
Given that the customer uses the company less than two times per month, what is the probability
that they expressed low satisfaction with the company?
Frequency of Use High
Satisfaction level
Medium Low TOTAL
< 2 per month 250 140 10 400
2 – 5 per month 140 55 5 200
> 5 per month 70 25 5 100
TOTAL 460 220 20 700
A) 41
70 B) 1
40 C) 1
70 D) 1
2
66)
67) The managers of a corporation were surveyed to determine the background that leads to a successful
manager. Each manager was rated as being either a good, fair, or poor manager by his/her boss. The
manager’s educational background was also noted. The data appear below. Given that a manager is only a
fair manager, what is the probability that this manager has no college background?
Educational Background
Manager
Rating H. S. Degree Some College College Degree Master’s or Ph.D. Totals
Good 5 6 24 4 39
Fair 8 18 44 17 87
Poor 3 2 1 28 34
Totals 16 26 69 49 160
A) 19
32 B) 1
2 C) 1
20 D) 8
87
67)
68) The managers of a corporation were surveyed to determine the background that leads to a successful
manager. Each manager was rated as being either a good, fair, or poor manager by his/her boss. The
manager’s educational background was also noted. The data appear below. Given that a manager is only a
fair manager, what is the probability that this manager has a college degree?
Educational Background
Manager
Rating H. S. Degree Some College College Degree Master’s or Ph.D. Totals
Good 4 2 28 5 39
Fair 8 14 41 24 87
Poor 7 5 3 19 34
Totals 19 21 72 48 160
A) 41
160 B) 24
29 C) 9
20 D) 41
87
68)
11
69) The managers of a corporation were surveyed to determine the background that leads to a successful
manager. Each manager was rated as being either a good, fair, or poor manager by his/her boss. The
manager’s educational background was also noted. The data appear below. Given that a manager is a
good manager, what is the probability that this manager has some college background?
Educational Background
Manager
Rating H. S. Degree Some College College Degree Master’s or Ph.D. Totals
Good 5 1 28 5 39
Fair 7 15 46 19 87
Poor 4 8 9 13 34
Totals 16 24 83 37 160
A) 1
24 B) 28
39 C) 1
39 D) 1
160
69)
70) A study was recently done that emphasized the problem we all face with drinking and driving.
Four hundred accidents that occurred on a Saturday night were analyzed. Two items noted were
the number of vehicles involved and whether alcohol played a role in the accident. The numbers
are shown below. Given that an accident involved multiple vehicles, what is the probability that it
involved alcohol?
Number of Vehicles Involved
Did Alcohol Play a Role? 1 2 3 or more Totals
Yes 60 99 11 170
No 28 170 32 230
Totals 88 269 43 400
A) 55
156 B) 11
400 C) 11
40 D) 11
43
70)
71) A researcher at a large university wanted to investigate if a student’s seat preference was related in
any way to the gender of the student. The researcher divided the lecture room into three sections
(1-front, middle of the room, 2-front, sides of the classroom, and 3-back of the classroom, both
middle and sides) and noted where his students sat on a particular day of the class. The researcher’s
summary table is provided below. Suppose a person sitting in the front, middle portion of the class is
randomly selected to answer a question. Find the probability the person selected is a female.
Area (1) Area (2) Area (3) Total
Males 20 6 7 33
Females 13 12 14 39
Total 33 18 21 72
A) 13
33 B) 13
72 C) 1
3 D) 11
13
71)
72) The manager of a used car lot took inventory of the automobiles on his lot and constructed the
following table based on the age of his car and its make (foreign or domestic). A car was randomly
selected from the lot. Given that the car selected was a foreign car, what is the probability that it
was older than 2 years? Age of Car (in years)
Make 0 – 2 3 – 5 6 – 10 over 10 Total
Foreign 35 30 14 21 100
Domestic 44 26 12 18 100
Total 79 56 26 39 200
A) 13
20 B) 35
121 C) 65
121 D) 7
20
72)
12
73) The manager of a used car lot took inventory of the automobiles on his lot and constructed the
following table based on the age of his car and its make (foreign or domestic). A car was randomly
selected from the lot. Given that the car selected was a domestic car, what is the probability that it
was older than 2 years?
Age of Car (in years)
Make 0 – 2 3 – 5 6 – 10 over 10 Total
Foreign 40 23 10 27 100
Domestic 42 21 14 23 100
Total 82 44 24 50 200
A) 21
41 B) 41
100 C) 29
50 D) 21
100
73)
74) The manager of a used car lot took inventory of the automobiles on his lot and constructed the following
table based on the age of his car and its make (foreign or domestic).
Age of Car (in years)
Make 0 – 2 3 – 5 6 – 10 over 10 Total
Foreign 38 30 10 22 100
Domestic 43 28 13 16 100
Total 81 58 23 38 200
A car was randomly selected from the lot. Given that the car selected is older than two years old, find the
probability that it is not a foreign car.
A) 31
50 B) 57
100 C) 62
119 D) 57
119
74)
Find the indicated probability. Give your answer as a decimal rounded to the nearest thousandth.
75) A fast-food restaurant chain with 700 outlets in the United States describes the geographic location
of its restaurants with the accompanying table of percentages. A restaurant is to be chosen at
random from the 700 to test market a new style of chicken. Given that the restaurant is located in
the eastern United States, what is the probability it is located in a city with a population of at least
10,000?
Region
NE SE SW NW
<10,000 5% 6% 3% 0%
Population of City 10,000 – 100,000 15% 2% 12% 5%
>100,000 20% 4% 3% 25%
A) 0.212 B) 0.41 C) 0.788 D) 0.477
75)
76) After completing an inventory of three warehouses, a golf club shaft manufacturer described its stock of
12,246 shafts with the percentages given in the table. Suppose a shaft is selected at random from the 12,246
currently in stock, and the warehouse number and type of shaft are observed. Given that the shaft is
produced in warehouse 2, find the probability it has an extra stiff shaft.
Type of Shaft
Regular Stiff Extra Stiff
1 19% 8% 5%
Warehouse 2 14% 2% 33%
3 1% 18% 0%
A) 0.868 B) 0.54 C) 0.673 D) 0.611
76)
13
77) The breakdown of workers in a particular state according to their political affiliation and type of job held is
shown here. Suppose a worker is selected at random within the state and the worker’s political affiliation
and type of job are noted. Given the worker is a Democrat, what is the probability that the worker is in a
white collar job.
Political Affiliation
Republican Democrat Independent
White collar 19% 12% 18%
Type of job
Blue Collar 8% 13% 30%
A) 0.403 B) 0.48 C) 0.245 D) 0.194
77)
78) A local country club has a membership of 600 and operates facilities that include an 18-hole
championship golf course and 12 tennis courts. Before deciding whether to accept new members,
the club president would like to know how many members regularly use each facility. A survey of
the membership indicates that 65% regularly use the golf course, 41% regularly use the tennis
courts, and 8% use neither of these facilities regularly. Given that a randomly selected member uses
the tennis courts regularly, find the probability that they also use the golf course regularly.
A) 0.132 B) 0.341 C) 0.215 D) 0.152
78)
Provide an appropriate response.
79) There are 30 chocolates in a box, all identically shaped. There are 11 filled with nuts, 10 filled with
caramel, and 9 are solid chocolate. You randomly select one piece, eat it, and then select a second
piece. Are the given events independent or dependent?
A) dependent B) independent
79)
80) Numbered disks are placed in a box and one disk is selected at random. There are 6 red disks
numbered 1 through 6, and 7 yellow disks numbered 7 through 13. In an experiment a disk is
selected, the number and color noted, replaced, and then a second disk is selected. Are the given
events independent or dependent?
A) dependent B) independent
80)
81) After completing an inventory of three warehouses, a golf club shaft manufacturer described its
stock of 12, 246 shafts with percentages given in the table. Is the event of selecting a shaft
independent of the warehouse? Answer Yes or No.
A) No B) Yes
81)
Solve the problem.
82) Suppose that events E and F are independent, P(E) = 0.9 and P(F ) = 0.4. What is the P(E and F )?
A) 0.94 B) 0.36 C) 1.3 D) 0.036
82)
83) A single die is rolled twice. Find the probability of getting a 5 the first time and a 1 the second time.
Express the probability as a simplified fraction.
A) 1
6 B) 1
12 C) 1
3 D) 1
36
83)
84) You are dealt one card from a 52 card deck. Then the card is replaced in the deck, the deck is
shuffled, and you draw again. Find the probability of getting a picture card the first time and a
spade the second time. Express the probability as a simplified fraction.
A) 3
52 B) 1
13 C) 1
4 D) 3
13
84)
14
85) If you toss a fair coin 10 times, what is the probability of getting all heads? Express the probability
as a simplified fraction.
A) 1
2 B) 1
2048 C) 1
1024 D) 1
512
85)
86) A human gene carries a certain disease from the mother to the child with a probability rate of 51%.
That is, there is a 51% chance that the child becomes infected with the disease. Suppose a female
carrier of the gene has four children. Assume that the infections of the four children are
independent of one another. Find the probability that all four of the children get the disease from
their mother. Round to the nearest thousandth.
A) 0.06 B) 0.058 C) 0.068 D) 0.932
86)
87) A machine has four components, A, B, C, and D, set up in such a manner that all four parts must
work for the machine to work properly. Assume the probability of one part working does not
depend on the functionality of any of the other parts. Also assume that the probabilities of the
individual parts working are P(A) = P(B) = 0.92, P(C) = 0.9, and P(D) = 0.93. Find the probability
that the machine works properly. Round to the nearest ten-thousandth.
A) 0.7618 B) 0.7084 C) 0.77 D) 0.2916
87)
88) Suppose a basketball player is an excellent free throw shooter and makes 94% of his free throws
(i.e., he has a 94% chance of making a single free throw). Assume that free throw shots are
independent of one another. Suppose this player gets to shoot three free throws. Find the
probability that he misses all three consecutive free throws. Round to the nearest ten-thousandth.
A) 0.1694 B) 0.0002 C) 0.8306 D) 0.9998
88)
89) What is the probability that in three consecutive rolls of two fair dice, a person gets a total of 7,
followed by a total of 11, followed by a total of 7? Round to the nearest ten-thousandth.
A) 0.2876 B) 0.0012 C) 0.0015 D) 0.1667
89)
90) A bag contains 10 white, 12 blue, 13 red, 7 yellow, and 8 green wooded balls. A ball is selected
from the bag, its color noted, then replaced. You then draw a second ball, note its color and then
replace the ball. What is the probability of selecting 2 red balls? Round to the nearest
ten-thousandth.
A) 0.0624 B) 0.0676 C) 0.2600 D) 0.5200
90)
91) A bag contains 10 white, 12 blue, 13 red, 7 yellow, and 8 green wooded balls. A ball is selected
from the bag, its color noted, then replaced. You then draw a second ball, note its color and then
replace the ball. What is the probability of selecting one white ball and one blue ball? Round to the
nearest ten-thousandth.
A) 0.0088 B) 0.4400 C) 0.2200 D) 0.0480
91)
15
Select the appropriate distribution.
92) Select the distribution that appears to be closest to normal.
A)
B)
C)
D) None of the distributions appear to be normal or near-normal.
92)
16
93) Select the distribution that appears to be closest to normal.
A)
B)
C)
D) None of the distributions appear to be normal or near-normal.
93)
17
94) Select the distribution that appears to be closest to normal.
A)
B)
C)
D) None of the distributions appear to be normal or near-normal.
94)
18
95) Select the distribution that appears to be closest to normal.
A)
B)
C)
D) None of the distributions appear to be normal or near-normal.
95)
Provide an appropriate response.
96) Compare a graph of the normal density function with mean of 0 and standard deviation of 1 with a
graph of a normal density function with mean equal to 4 and standard deviation of 1. The graphs
would
A) Have the same height but one would be shifted 4 units to the right.
B) Have no horizontal displacement but one would be steeper that the other.
C) Have no horizontal displacement but one would be flatter than the other.
D) Have the same height but one would be shifter 4 units to the left.
96)
97) Compare a graph of the normal density function with mean of 0 and standard deviation of 1 with a
graph of a normal density function with mean equal to 0 and standard deviation of 0.5. The graphs
would
A) Have the same height but one would be shifted 4 units to the right.
B) Have no horizontal displacement but one would be steeper that the other.
C) Have no horizontal displacement but one would be flatter than the other.
D) Have the same height but one would be shifter 4 units to the left.
97)
19
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
98) The SAT is an exam used by colleges and universities to evaluate undergraduate
applicants. The test scores are normally distributed. In a recent year, the mean test score
was 1484 and the standard deviation was 298. The test scores of four students selected at
random are 1930, 1340, 2150, and 1450. Find the z-scores that correspond to each value.
98)
99) The ACT is an exam used by colleges and universities to evaluate undergraduate
applicants. The test scores are normally distributed. In a recent year, the mean test score
was 23 and the standard deviation was 5.2. The test scores of four students selected at
random are 16, 24, 9, and 35. Find the z-scores that correspond to each value.
99)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the probability that a z-score randomly selected from the normal distribution meets the given condition.
100) The z-score is less than 1.5.
A) 0.5199 B) 0.7612 C) 0.0668 D) 0.9332
100)
101) The z-score is less than 1.25.
A) 0.8944 B) 0.7682 C) 0.1056 D) 0.2318
101)
102) The z-score is greater than 1.
A) 0.5398 B) 0.1397 C) 0.8413 D) 0.1587
102)
103) The z-score is greater than -1.25.
A) 0.7193 B) 0.8944 C) 0.5843 D) 0.6978
103)
104) The z-score is between 0 and 3.
A) 0.9987 B) 0.4987 C) 0.4641 D) 0.0010
104)
105) The z-score is between 1 and 2.
A) 0.8413 B) 0.5398 C) 0.2139 D) 0.1359
105)
106) The z-score is between -1.5 and 2.5.
A) 0.6312 B) 0.9270 C) 0.9831 D) 0.7182
106)
107) The z-score is between 1.5 and 2.5.
A) 0.9816 B) 0.0606 C) 0.9938 D) 0.9332
107)
108) The z-score is between -1.25 and 1.25.
A) 0.8817 B) 0.7888 C) 0.6412 D) 0.2112
108)
Provide an appropriate response.
109) A physical fitness association is including the mile run in its secondary-school fitness test. The time
for this event for boys in secondary school is known to possess a normal distribution with a mean
of 440 seconds and a standard deviation of 40 seconds. Find the probability that a randomly
selected boy in secondary school can run the mile in less than 348 seconds.
A) 0.5107 B) 0.4893 C) 0.9893 D) 0.0107
109)
20
110) A physical fitness association is including the mile run in its secondary-school fitness test. The time
for this event for boys in secondary school is known to possess a normal distribution with a mean
of 450 seconds and a standard deviation of 50 seconds. Find the probability that a randomly
selected boy in secondary school will take longer than 335 seconds to run the mile.
A) 0.9893 B) 0.0107 C) 0.5107 D) 0.4893
110)
111) Suppose a brewery has a filling machine that fills 12 ounce bottles of beer. It is known that the
amount of beer poured by this filling machine follows a normal distribution with a mean of
12.38 ounces and a standard deviation of 0.04 ounce. Find the probability that the bottle contains
fewer than 12.28 ounces of beer.
A) 0.9938 B) 0.0062 C) 0.4938 D) 0.5062
111)
112) Suppose a brewery has a filling machine that fills 12 ounce bottles of beer. It is known that the
amount of beer poured by this filling machine follows a normal distribution with a mean of 10.14
onces and a standard deviation of 0.04 ounce. Find the probability that the bottle contains more
than 10.14 ounces of beer.
A) 1 B) 0.4 C) 0.5 D) 0
112)
113) Suppose a brewery has a filling machine that fills 12 ounce bottles of beer. It is known that the
amount of beer poured by this filling machine follows a normal distribution with a mean of
12.29 ounces and a standard deviation of 0.04 ounce. Find the probability that the bottle contains
between 12.19 and 12.25 ounces.
A) 0.1525 B) 0.1649 C) 0.8351 D) 0.8475
113)
114) The length of time it takes college students to find a parking spot in the library parking lot follows a
normal distribution with a mean of 4.5 minutes and a standard deviation of 1 minute. Find the
probability that a randomly selected college student will find a parking spot in the library parking
lot in less than 4.0 minutes.
A) 0.3085 B) 0.2674 C) 0.1915 D) 0.3551
114)
115) The length of time it takes college students to find a parking spot in the library parking lot follows a
normal distribution with a mean of 6.0 minutes and a standard deviation of 1 minute. Find the
probability that a randomly selected college student will take between 4.5 and 7.0 minutes to find a
parking spot in the library lot.
A) 0.0919 B) 0.4938 C) 0.7745 D) 0.2255
115)
116) The amount of soda a dispensing machine pours into a 12 ounce can of soda follows a normal
distribution with a mean of 12.06 ounces and a standard deviation of 0.04 ounce. The cans only
hold 12.10 ounces of soda. Every can that has more than 12.10 ounces of soda poured into it causes
a spill and the can needs to go through a special cleaning process before it can be sold. What is the
probability a randomly selected can will need to go through this process?
A) 0.8413 B) 0.3413 C) 0.1587 D) 0.6587
116)
117) A new phone system was installed last year to help reduce the expense of personal calls that were
being made by employees. Before the new system was installed, the amount being spent on
personal calls followed a normal distribution with an average of $600 per month and a standard
deviation of $50 per month. Refer to such expenses as PCE’s (personal call expenses). Using the
distribution above, what is the probability that a randomly selected month had a PCE of between
$475.00 and $690.00?
A) 0.0421 B) 0.0001 C) 0.9579 D) 0.9999
117)
21
118) A new phone system was installed last year to help reduce the expense of personal calls that were
being made by employees. Before the new system was installed, the amount being spent on
personal calls follows a normal distribution with an average of $700 per month and a standard
deviation of $50 per month. Refer to such expenses as PCE’s (personal call expenses). Find the
probability that a randomly selected month had a PCE that falls below $550.
A) 0.0013 B) 0.7857 C) 0.9987 D) 0.2143
118)
119) The tread life of a particular brand of tire is a random variable best described by a normal
distribution with a mean of 60,000 miles and a standard deviation of 2000 miles. What is the
probability a particular tire of this brand will last longer than 58,000 miles?
A) 0.8413 B) 0.2266 C) 0.7266 D) 0.1587
119)
120) The tread life of a particular brand of tire is a random variable best described by a normal
distribution with a mean of 60,000 miles and a standard deviation of 1700 miles. What is the
probability a certain tire of this brand will last between 56,430 miles and 56,940 miles?
A) 0.4649 B) 0.4920 C) 0.9813 D) 0.0180
120)
121) IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. What is
the IQ that corresponds to a z-score of 2.33?
A) 134.95 B) 125.95 C) 142.35 D) 139.55
121)
122) IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. What is
the IQ that corresponds to a z-score of -1.645?
A) 91.0 B) 79.1 C) 82.3 D) 75.3
122)
123) The scores on a mathematics exam have a mean of 66 and a standard deviation of 6. What is the
exam score that corresponds to the z-score -1.645?
A) 64.4 B) 60.0 C) 75.9 D) 56.1
123)
124) Assume that the salaries of elementary school teachers in the United States are normally distributed
with a mean of $40,000 and a standard deviation of $4000. What is the cutoff salary for teachers in
the bottom 10%?
A) $45,120 B) $34,880 C) $33,420 D) $46,580
124)
125) The body temperatures of adults are normally distributed with a mean of 98.6° F and a standard
deviation of 0.95° F. What temperature represents the 95th percentile?
A) 100.16° F B) 100.46° F C) 97.04° F D) 99.82° F
125)
126) A tire company finds the lifespan for one brand of its tires is normally distributed with a mean of
46,900 miles and a standard deviation of 4000 miles. If the manufacturer is willing to replace no
more than 10% of the tires, what should be the approximate number of miles for a warranty?
A) 52,020 B) 53,480 C) 41,780 D) 40,320
126)
127) Compare the scores: a score of 75 on a test with a mean of 65 and a standard deviation of 8 and a
score of 75 on a test with a mean of 70 and a standard deviation of 4.
A) A score of 75 with a mean of 70 and a standard deviation of 4 is better.
B) The two scores are statistically the same.
C) A score of 75 with a mean of 65 and a standard deviation of 8 is better.
D) You cannot determine which score is better from the given information.
127)
22
128) Compare the scores: a score of 88 on a test with a mean of 79 and a score of 78 on a test with a mean
of 70.
A) A score of 75 with a mean of 65 and a standard deviation of 8 is better.
B) You cannot determine which score is better from the given information.
C) The two scores are statistically the same.
D) A score of 75 with a mean of 70 and a standard deviation of 4 is better.
128)
129) Compare the scores: a score of 220 on a test with a mean of 200 and a standard deviation of 21 and a
score of 90 on a test with a mean of 80 and a standard deviation of 8.
A) A score of 90 with a mean of 80 and a standard deviation of 8 is better.
B) A score of 220 with a mean of 200 and a standard deviation of 21 is better.
C) You cannot determine which score is better from the given information.
D) The two scores are statistically the same.
129)
130) Two high school students took equivalent language tests, one in German and one in French. The
student taking the German test, for which the mean was 66 and the standard deviation was 8,
scored an 82, while the student taking the French test, for which the mean was 27 and the standard
deviation was 5, scored a 35. Compare the scores.
A) A score of 35 with a mean of 27 and a standard deviation of 5 is better.
B) The two scores are statistically the same.
C) A score of 82 with a mean of 66 and a standard deviation of 8 is better.
D) You cannot determine which score is better from the given information.
130)
131) SAT scores have a mean of 1026 and a standard deviation of 209. ACT scores have a mean of 20.8
and a standard deviation of 4.8. A student takes both tests while a junior and scores 1130 on the
SAT and 25 on the ACT. Compare the scores.
A) A score of 1130 on the SAT test was better.
B) You cannot determine which score is better from the given information.
C) The two scores are statistically the same.
D) A score of 25 on the ACT test was better.
131)
132) SAT scores have a mean of 1026 and a standard deviation of 209. ACT scores have a mean of 20.8
and a standard deviation of 4.8. A student takes both tests while a junior and scores 860 on the SAT
and 16 on the ACT. Compare the scores.
A) A score of 860 on the SAT test was better.
B) A score of 16 on the ACT test was better.
C) You cannot determine which score is better from the given information.
D) The two scores are statistically the same.
132)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
133) The SAT is an exam used by colleges and universities to evaluate undergraduate
applicants. The test scores are normally distributed. In a recent year, the mean test score
was 1490 and the standard deviation was 292. The test scores of four students selected at
random are 1930, 1340, 2150, and 1450.
a) Find the z-scores that correspond to each value
b) Determine whether any of the values are unusual.
133)
23
134) The ACT is an exam used by colleges and universities to evaluate undergraduate
applicants. The test scores are normally distributed. In a recent year, the mean test score
was 22 and the standard deviation was 5. The test scores of four students selected at random
are 16, 24, 9, and 35.
a) Find the z-scores that correspond to each value.
b) Determine whether any of the values are unusual.
134)
24
Answer Key
Testname: UNTITLED5
1) A
2) A
3) A
4) B
5) B
6) A
7) Answers to parts (a) and (b) will vary.
The answer in part (b) is likely to be closer to the classical probability of 1
4 .
In general, as the number of repetitions of a probability experiment increases, the
closer the empirical probability should get to the classical probability.
8) Answers to parts (a) and (b) will vary.
The answer in part (b) is likely to be closer to the classical probability of 1
4 .
In general, as the number of repetitions of a probability experiment increases, the
closer the empirical probability should get to the classical probability.
9) B
10) C
11) B
12) B
13) C
14) D
15) B
16) B
17) D
18) C
19) D
20) D
21) A
22) A
23) B
24) A
25) C
26) D
27) C
28) 0.215
29) 0.914
30) B
31) D
32) A
33) B
34) C
35) D
36) A
37) C
38) C
39) D
25
Answer Key
Testname: UNTITLED5
40) D
41) D
42) C
43) A
44) B
45) A
46) B
47) B
48) C
49) D
50) B
51) A
52) D
53) B
54) B
55) D
56) B
57) B
58) A
59) C
60) B
61) A
62) C
63) A
64) A
65) D
66) B
67) D
68) D
69) C
70) A
71) A
72) A
73) C
74) D
75) C
76) C
77) B
78) B
79) A
80) B
81) A
82) B
83) D
84) A
85) C
86) C
87) B
88) B
89) C
26
Answer Key
Testname: UNTITLED5
90) B
91) D
92) C
93) A
94) C
95) D
96) A
97) B
98) x = 1930 → z ≈ 1.50
x = 1340 → z ≈ -0.48
x = 2150 → z ≈ 2.23
x = 1450 → z ≈ -0.11
99) x = 16 → z ≈ -1.35
x = 24 → z ≈ 0.19
x = 9 → z ≈ -2.69
x = 35 → z ≈ 2.31
100) D
101) A
102) D
103) B
104) B
105) D
106) B
107) B
108) B
109) D
110) A
111) B
112) C
113) A
114) A
115) C
116) C
117) C
118) A
119) A
120) D
121) A
122) D
123) D
124) B
125) A
126) C
127) B
128) B
129) A
130) C
131) D
132) A
27
Answer Key
Testname: UNTITLED5
133) a) x = 1930 → z ≈ 1.51
x = 1340 → z ≈ -0.51
x = 2150 → z ≈ 2.26
x = 1450 → z ≈ -0.14
b) x = 2150 is unusual because its corresponding z-score (2.26) lies more than 1.96 standard deviations from the mean.
134) a) x = 16 → z ≈ -1.20
x = 24 → z ≈ 0.40
x = 9 → z ≈ -2.60
x = 35 → z ≈ 2.60
b) x = 9 is unusual because its corresponding z-score (-2.60) lies more than 1.96 standard deviations from the mean.
x = 35 is unusual because its corresponding z-score (2.60) lies more than 1.96 standard deviations from the mean.
28

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