Elementary Statistics
Review Problems for Exam 2 (Please show work)
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem. Round results to the nearest hundredth.
1) The mean of a set of data is 4.68 and its standard deviation is 2.83. Find the z score for a value of
9.38.
A) 1.49
B) 1.66
C) 1.96
D) 1.83
Determine which score corresponds to the higher relative position.
2) Which is better: a score of 82 on a test with a mean of 70 and a standard deviation of 8, or a score of
82 on a test with a mean of 75 and a standard deviation of 4?
A) The second 82
B) The first 82
C) Both scores have the same relative position.
Find the percentile for the data point.
3) In a data set with a range of 66.5 to 121.4 and 200 observations, there are 138 data points with
values less than 87.7. Find the percentile for 87.7.
A) 32
B) 69
C) 424
D) 138.43
Find the indicated measure.
4) The weights (in pounds) of 30 newborn babies are listed below. Find Q1 .
5.5 5.7 5.8 6.0 6.1 6.1 6.3 6.4 6.5 6.6
6.7 6.7 6.7 6.9 7.0 7.0 7.0 7.1 7.2 7.2
7.4 7.5 7.7 7.7 7.8 8.0 8.1 8.1 8.3 8.7
A) 5.8
B) 7.5
C) 6.3
1)
2)
3)
4)
D) 6.4
Find the indicated probability.
5) 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
A)
B) 7
C) 0
D) 1
7
Answer the question, considering an event to be "unusual" if its probability is less than or equal to 0.05.
6) Is it "unusual" to get 9 when a pair of dice is rolled?
A) Yes
B) No
Estimate the probability of the event.
7) Of 1338 people who came into a blood bank to give blood, 253 people had high blood pressure.
Estimate the probability that the next person who comes in to give blood will have high blood
pressure.
A) 0.157
B) 0.24
C) 0.108
D) 0.189
5)
6)
7)
Construct a boxplot for the given data. Include values of the 5-number summary in all boxplots.
8) The test scores of 32 students are listed below. Construct a boxplot for the data set.
32 37 41 44 46 48 53 55
57 57 59 63 65 66 68 69
70 71 74 74 75 77 78 79
81 82 83 86 89 92 95 99
A)
8)
B)
C)
D)
From the information provided, create the sample space of possible outcomes.
9) Flip a coin three times.
A) HHH HTT HTH TTT HTT THH HHT THT
B) HHH TTT THT HTH HHT TTH HTH
C) HHH HHT HTH HTT THH THT TTH TTT
D) HTT THT HTH HHH TTH TTT
Determine whether the events are mutually exclusive.
10) Meet a man with an umbrella.
Meet a man with a raincoat.
A) No
B) Yes
Find the indicated probability.
11) Find P(A), given that P(A) = 0.662.
A) 1.662
B) 1.511
C) 0
9)
10)
11)
D) 0.338
12) The table below describes the smoking habits of a group of asthma sufferers.
Occasional Regular Heavy
Nonsmoker
smoker
smoker smoker Total
Men
433
42
71
37
583
Women
326
47
78
39
490
Total
759
89
149
76
1073
If one of the 1073 people is randomly selected, find the probability that the person is a man or a
heavy smoker.
A) 0.487
B) 0.614
C) 0.545
D) 0.580
12)
13) 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.
13)
Waiting Time Number of
(minutes) Customers
0-3
13
4-7
10
8-11
11
12-15
5
16-19
4
20-23
2
24-27
3
If we randomly select one of the customers represented in the table, what is the probability that the
waiting time is at least 12 minutes or between 8 and 15 minutes?
A) 0.521
B) 0.104
C) 0.727
D) 0.625
14) A card is drawn from a well-shuffled deck of 52 cards. Find P(drawing a face card or a 4).
4
2
12
A)
B)
C)
D) 16
13
13
13
Is Event B dependent or independent of Event A?
15) A: A green ball is drawn from a box with five balls and placed next to the box.
B: A red ball is drawn next and placed next to the green one.
A) Dependent
B) Independent
Find the indicated probability.
16) Find the probability of correctly answering the first 2 questions on a multiple choice test if random
guesses are made and each question has 3 possible answers.
1
3
1
2
A)
B)
C)
D)
9
2
8
3
14)
15)
16)
17) A batch consists of 12 defective coils and 88 good ones. Find the probability of getting two good
coils when two coils are randomly selected if the first selection is replaced before the second is
made.
A) 0.176
B) 0.7744
C) 0.7733
D) 0.0144
17)
18) You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing
cards. Find the probability that the first card is a King and the second card is a queen.
2
13
1
4
A)
B)
C)
D)
13
102
663
663
18)
19) A IRS auditor randomly selects 3 tax returns from 57 returns of which 6 contain errors. What is the
probability that she selects none of those containing errors?
A) 0.0012
B) 0.7163
C) 0.0007
D) 0.7117
19)
20) A study conducted at a certain college shows that 53% of the school's graduates find a job in their
chosen field within a year after graduation. Find the probability that among 7 randomly selected
graduates, at least one finds a job in his or her chosen field within a year of graduating.
A) 0.143
B) 0.995
C) 0.530
D) 0.988
20)
21) The table below shows the soft drinks preferences of people in three age groups.
cola root beer lemon-lime
under 21 years of age 40
25
20
between 21 and 40 35
20
30
over 40 years of age 20
30
35
21)
If one of the 255 subjects is randomly selected, find the probability that the person is over 40 and
drinks cola.
4
4
A)
B)
51
19
C)
4
17
D) None of the above is correct.
22) The table below shows the soft drinks preferences of people in three age groups.
cola root beer lemon-lime
under 21 years of age 40
25
20
between 21 and 40 35
20
30
over 40 years of age 20
30
35
22)
If one of the 255 subjects is randomly selected, find the probability that the person drinks root beer
given that they are over 40.
2
2
A)
B)
5
17
C)
6
17
D) None of the above is correct.
Evaluate the expression.
23) 5 P4
A) 5
B) 24
C) 1
D) 120
24) 10C2
A) 40,320
B) 45
C) 80,640
D) 5
23)
24)
Solve the problem.
25) How many ways can an IRS auditor select 4 of 10 tax returns for an audit?
A) 24
B) 210
C) 5040
25)
D) 10,000
26) A pollster wants to minimize the effect the order of the questions has on a person's response to a
survey. How many different surveys are required to cover all possible arrangements if there are 5
questions on the survey?
A) 120
B) 25
C) 5
D) 24
Evaluate the expression.
10!
27)
4!
A)
5
2
26)
27)
B) 40,000
C) 2!
D) 151,200
28) 2!
28)
A) 2
B) 4
C) 0
D) 1
Identify the given random variable as being discrete or continuous.
29) The pH level in a shampoo
A) Discrete
B) Continuous
29)
30) The number of phone calls between New York and California on Thanksgiving day
A) Discrete
B) Continuous
30)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Determine whether the following is a probability distribution. If not, identify the requirement that is not satisfied.
31)
31)
x P(x)
1 0.037
2 0.200
3 0.444
4 0.296
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the mean of the given probability distribution.
32) The number of golf balls ordered by customers of a pro shop has the following probability
distribution.
x
3
6
9 12 15
p(x) 0.14 0.11 0.36 0.29 0.10
A) 8.22
B) 6.63
C) 9.3
D) 9
Solve the problem.
33) Find the standard deviation for the given probability distribution.
x P(x)
0 0.37
1 0.05
2 0.13
3 0.25
4 0.20
A) 1.60
B) 2.45
C) 2.56
32)
33)
D) 1.71
34) A police department reports that the probabilities that 0, 1, 2, and 3 burglaries will be reported in a
given day are 0.52, 0.40, 0.07, and 0.01, respectively. Find the standard deviation for the probability
distribution. Round answer to the nearest hundredth.
A) 0.88
B) 0.67
C) 0.45
D) 0.98
34)
35) 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) -$0.50
C) -$0.40
D) $0.00
35)
36) A company manufactures batteries in batches of 28 and there is a 3% rate of defects. Find the
standard deviation for the number of defects per batch.
A) 0.917
B) 0.9
C) 0.886
D) 0.903
36)
Determine whether the given procedure results in a binomial distribution. If not, state the reason why.
37) Choosing 5 people (without replacement) from a group of 59 people, of which 15 are women,
keeping track of the number of men chosen.
A) Not binomial: there are more than two outcomes for each trial.
B) Not binomial: the trials are not independent.
C) Procedure results in a binomial distribution.
D) Not binomial: there are too many trials.
37)
38) Spinning a roulette wheel 7 times, keeping track of the occurrences of a winning number of "16".
A) Not binomial: the trials are not independent.
B) Procedure results in a binomial distribution..
C) Not binomial: there are more than two outcomes for each trial.
D) Not binomial: there are too many trials.
38)
39) Rolling a single die 46 times, keeping track of the "fives" rolled.
A) Not binomial: there are too many trials.
B) Not binomial: there are more than two outcomes for each trial.
C) Procedure results in a binomial distribution.
D) Not binomial: the trials are not independent.
39)
Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability
formula to find the probability of x successes given the probability p of success on a single trial.
40) n = 5, x = 2, p = 0.70
40)
A) 0.132
B) 0.198
C) 0.464
D) 0.700
Find the indicated probability.
41) In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are
selected at random from the physics majors, that is the probability that no more than 6 belong to an
ethnic minority?
A) 0.9815
B) 0.0547
C) 0.9846
D) 0.913
42) The participants in a television quiz show are picked from a large pool of applicants with
approximately equal numbers of men and women. Among the last 11 participants there have been
only 2 women. If participants are picked randomly, what is the probability of getting 2 or fewer
women when 11 people are picked?
A) 0.0322
B) 0.0327
C) 0.0059
D) 0.0269
41)
42)
Find the mean, μ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth.
43) n = 20; p = 3/5
43)
A) μ = 12.0
B) μ = 11.5
C) μ = 12.7
D) μ = 12.3
Find the standard deviation, σ, for the binomial distribution which has the stated values of n and p. Round your answer
to the nearest hundredth.
44) n = 25; p = 3/5
44)
A) σ = 6.57
B) σ = 0.04
C) σ = 2.45
D) σ = 5.72
Solve the problem.
45) On a multiple choice test with 11 questions, each question has four possible answers, one of which
is correct. For students who guess at all answers, find the mean for the number of correct answers.
A) 8.3
B) 3.7
C) 5.5
D) 2.8
45)