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Part III: Sample Chapter Tests and Answers
CHAPTER 5 TEST
95
FORM A
PAGE 1
1. Sam is a representative who sells large appliances such as
refrigerators, stoves, and so forth. Let x = number of appliances Sam sells on a given day. Let f = frequency with which
he sells x appliances. For a random sample of 240 days,
Sam had the following sales record.
x
0
1
2
3
4
5
6
7
f
9
72
63
41
28
14
8
5
Assume that the sales record is representative of the population
of all sales days.
(a) Use the relative frequency to find P(x) for x = 0 to 7.
(b) Use a histogram to graph the probability distribution
of part (a).
1. (a) __________________________
(b)
(c) Compute the probability that x is between 2 and 5
(including 2 and 5).
(c) __________________________
(d) Compute the probability that x is less than 3.
(d) __________________________
(e) Compute the expected value of the x distribution.
(e) __________________________
(f) Compute the standard deviation of the x distribution.
(f)_ __________________________
2. The director of a health club conducted a survey and found
that 23% of members used only the pool for workouts. Based
on this information, what is the probability that, for a random
sample of 10 members, 4 used only the pool for workouts?
2. ______________________________
3. Of those mountain climbers who attempt Mt. McKinley,
only 65% reach the summit. In a random sample of
16 mountain climbers who are going to attempt Mt. McKinley,
what is the probability of each of the following?
(a) All 16 reach the summit.
3. (a) __________________________
(b) At least 10 reach the summit.
(b) __________________________
(c) No more than 12 reach the summit.
(c) __________________________
(d) From 9 to 12 reach the summit, including 9 and 12.
(d) __________________________
Copyright © Houghton Mifflin Company. All rights reserved.
Instructor's Resource Guide Understandable Statistics, 9/e
96
CHAPTER 5 TEST
FORM A
PAGE 2
4. A coach found that about 12% of all hockey games end
in overtime. What is the expected number of games ending in overtime if 50 hockey games are played as a
random sample?
4. _____________________________
5. There is about 75% probability that a truck will be going
over the speed limit on I-80 between Cheyenne and Rock
Springs, Wyoming. Suppose that a random sample of five
trucks on this stretch of I-80 is observed.
(a) Make a histogram showing the probability that
r = 0, 1, 2, 3, 4, 5 trucks are speeding.
5. (a)
(b) Find the mean  of this probability distribution.
(b) __________________________
(c) Find the standard deviation of this probability
distribution.
(c) __________________________
6. Records show that the probability of catching a northern pike over 40 inches at Taltson Lake (Canada) is
about 15% for each full day a person spends fishing.
What is the minimum number of days a person must
fish to be at least 83.3% sure of catching one or more
northern pike over 40 inches?
6. _____________________________
7. We are interested in when the first six will occur for
repeated rolls of a balanced die. What is the population mean for this geometric distribution (i.e., the
expected number of rolls for the first 6 to occur)?
7. _____________________________
Copyright © Houghton Mifflin Company. All rights reserved.
Part III: Sample Chapter Tests and Answers
CHAPTER 5 TEST
97
FORM A
PAGE 3
8. The probability that an airplane is more than 45 minutes late
on arrival is about 15%. Let n = 1, 2, 3, … represent the
number of times a person travels on an airplane until the first
time the plane is more than 45 minutes late.
(a) Write a brief but complete discussion in which you explain
why the geometric distribution would be appropriate. Write
out a formula for the probability distribution of the random
variable n.
8. (a) __________________________
(b) What is the probability that the third time a person flies is the
first time the person is late by more the 45 minutes?
(b) __________________________
(c) What is the probability that more than three flights are required before a plane is more than 45 minutes late?
(c) __________________________
9. Suppose that the average number of customers entering a store in a
20-minute period is six customers. The store wants a probability
distribution for the number of people entering the store each 20
minutes.
(a) Write a brief but complete discussion in which you explain
why the Poisson approximation to the binomial would be
appropriate. Are the assumptions satisfied? What is ?
Write out a formula for the probability distribution of r.
(b) What is the probability that exactly three customers enter the
store during a 20-minute period?
9. (a) __________________________
(b) __________________________
(c) What is the probability that more than three customers enter the
store during a 20-minute period?
(c) __________________________
10. The probability that a new medication will cause a bad side effect
is 0.03. The new medication has been given to 150 volunteers.
Let r be the random variable representing the number of people
who have a bad side effect.
(a) Write a brief but complete discussion in which you explain
why the Poisson approximation to the binomial would be
appropriate. Are the assumptions satisfied? What is ?
Write out a formula for the probability distribution of r.
10. (a) __________________________
(b) Compute the probability that exactly 3 people from the
sample of 150 volunteers will have a bad side effect from
the medication.
(b) __________________________
(c) Compute the probability that more than 3 people from the
sample of 150 volunteers will have a bad side effect from
the medication.
(c) __________________________
Copyright © Houghton Mifflin Company. All rights reserved.
Instructor's Resource Guide Understandable Statistics, 9/e
98
CHAPTER 5 TEST
FORM B
PAGE 1
1. An aptitude test was given to a random sample of 228 people
intending to become data-entry clerks. The results are shown
below, where x is the score on a 10-point scale and f is the
frequency of people with this score.
x
1
2
3
4
5
6
7
8
9
10
f
9
21
46
51
42
18
12
10
8
5
Assume that these data represent the entire population of
people intending to become data-entry clerks.
(a) Use the relative frequencies to find P(x) for x = 1 to x = 10.
(b) Use a histogram to graph the probability distribution
of part (a).
1. (a) __________________________
(b)
(c) To be accepted into a training program, students must have
a score of 4 or higher. What is the probability that an
applicant selected at random will have this score?
(c) __________________________
(d) To receive a tuition scholarship, a student needs a score of
8 or higher. What is the probability that an applicant selected
at random will have such a score?
(d) __________________________
(e) Compute the expected value of the x distribution.
(e) __________________________
(f) Compute the standard deviation of the x distribution.
(f) __________________________
2. The management of a restaurant conducted a survey and found
that 28% of the customers preferred to sit in the smoking section.
Based on this information, what is the probability that for a
random sample of 12 customers, 3 preferred the smoking
section?
2. _____________________________
3. Of all college freshmen who try out for the track team, the
coach will only accept 30%. If 15 freshmen try out for the
track team, what is the probability that
(a) all 15 are accepted?
3. (a) __________________________
(b) at least 8 are accepted?
(b) __________________________
(c) no more than 4 are accepted?
(c) __________________________
(d) between 5 and 10 are accepted (including 5 and 10)?
(d) __________________________
Copyright © Houghton Mifflin Company. All rights reserved.
Part III: Sample Chapter Tests and Answers
CHAPTER 5 TEST
99
FORM B
4. The president of a bank approves 68% of all new applications.
What is the expected number of approvals if 75 loan
applications are chosen at random?
PAGE 2
4. _____________________________
5. The probability that a vehicle will change lanes while making
a turn is 55%. Suppose that a random sample of seven vehicles is
observed making turns at a busy intersection.
(a) Make a histogram showing the probability that
r = 0, 1, 2, 3, 4, 5, 6, 7 vehicles will make a lane change
while turning.
5. (a)
(b) Find the expected value  of this probability distribution.
(b) __________________________
(c) Find the standard deviation of this probability
distribution.
(c) __________________________
6. Past records show that the probability of catching a lake
trout over 15 pounds at Talston Lake (Canada) is about
20% for each full day a person spends fishing. What is
the minimal number of days a person must fish to be at
least 89.3% sure of catching one or more lake trout over
15 pounds?
6. _____________________________
7. We are interested in when the first odd number will occur
for repeated rolls of a balanced die. What is the population
mean for this geometric distribution (i.e., the expected number
of rolls for the first odd number to occur)?
7. _____________________________
Copyright © Houghton Mifflin Company. All rights reserved.
Instructor's Resource Guide Understandable Statistics, 9/e
100
CHAPTER 5 TEST
FORM B
PAGE 3
8. Past records at an appliance store show that about 60% of the customers who look at appliances will buy. Let n = 1, 2, 3, …
represent the number of customers a sales clerk must help until
the first sale of the day.
(a) Write a brief but complete discussion in which you explain
why the geometric distribution would apply in this context.
Write out a formula for the probability distribution of the
random variable n.
8. (a) __________________________
(b) Compute P(n = 4).
(b) __________________________
(c) Compute P(n  3).
(c) __________________________
9. At Community Hospital maternity ward, babies arrive at an
average of eight babies per day. The hospital staff wants a
probability distribution for the number of babies arriving
each day.
(a) Write a brief but complete discussion in which you explain
why the Poisson distribution would be appropriate. What
is ? Write out a formula for the probability distribution.
9. (a) __________________________
(b) What is the probability that exactly seven babies are born
during the next day?
(b) __________________________
(c) What is the probability that fewer than three babies are born
during the next day?
(c) __________________________
10. As a telecommunications satellite goes over the horizon, stored
messages are relayed to the next satellite, which is still in position.
However, the probability is 0.01 that an interruption will occur,
and the relay transmission will be lost. Of 200 such relays,
let r be the random variable that represents the number of transmissions that are lost.
(a) Write a brief but complete discussion in which you explain
why the Poisson approximation to the binomial would be
appropriate. Are the assumptions satisfied? What is ?
Write out a formula for the probability distribution of r.
10. (a) __________________________
(b) Compute the probability that exactly two transmissions
are lost.
(b) __________________________
(c) Compute the probability that more than two transmissions
are lost.
(c) __________________________
Copyright © Houghton Mifflin Company. All rights reserved.
Part III: Sample Chapter Tests and Answers
CHAPTER 5 TEST
101
FORM C
PAGE 1
Write the letter of the response that best answers each problem.
1.
The following data are based on a survey taken by a consumer research firm.
In this table, x = number of televisions in household and % = percentages of
U.S. households.
x
0
1
2
3
4
5 or more
%
3%
11%
28%
39%
12%
7%
A. What is the probability that a household selected at random has less than
three televisions?
(a) 0.81
(b) 0.39
(c) 0.42
(d) 0.58
(e) 0.19
B. What is the probability that a household selected at random has more than
four televisions?
(a) 0.7
(b) 0.19
(c) 0.81
(d) 0.93
(b) 2.67
(c) 1.28
(d) 1.13
2.
(c) 1.28
(d) 1.13
(b) 0.67
(c) 0.28
(d) 0.13
D. __________
(e) 3.1
A meteorologist found from the past year’s records that it rained 17% of the days.
Based on this information, what is the probability that, for a random sample of 15
days, it rained 3 of those days?
(a) 0.17
3.
(b) 2.67
C. __________
(e) 3.1
D. Compute the standard deviation of the x distribution (round televisions of five
or more to five).
(a) 15
B. __________
(e) 0.07
C. Compute the expected value of the x distribution (round televisions of five or
more to five).
(a) 15
1. A. __________
2. _____________
(e) 0.24
Of those people who lose weight on a diet, 90% gain all the weight back. In a
random sample of 12 dieters who have lost weight, what is the probability of
each of the following?
A. All 12 gain the weight back.
(a) 0.90
(b) 0.282
3. A. __________
(c) 0.540
(d) 0.142
(e) 10.8%
B. At least 9 gain the weight back.
(a) 0.974
(b) 0.026
(c) 0.889
B. __________
(d) 1.33%
(e) 0.997
C. No more than 6 gain the weight back.
(a) 0.004
(b) 1.000
(c) 0.999
C. __________
(d) 0.000
(e) 0.531
D. From 8 to 10 gain the weight back, including 8 and 10.
(a) 0.085
(b) 1.17%
(c) 0.336
Copyright © Houghton Mifflin Company. All rights reserved.
(d) 0.387
D. __________
(e) 0.118
Instructor's Resource Guide Understandable Statistics, 9/e
102
CHAPTER 5 TEST
FORM C
PAGE 2
4. The manager of a supermarket found that 72% of the shoppers who taste a free
sample of a food item will buy the item. What is the expected number of shoppers
that will buy the item if 50 randomly selected shoppers taste a free sample?
(a) 10
(b) 36
(c) 3
(d) 72
4. _____________
(e) 50
5. The probability that merchandise stolen from a store will be recovered is 15%. Suppose
that a random sample of eight stores, from which merchandise has been stolen, is chosen.
A. Find the mean  of this probability distribution.
(a) 1.02
(b) 1.07
(c) 1.01
5. A. __________
(d) 1.14
(e) 1.2
B. Find the standard deviation of this probability distribution.
(a) 1.02
(b) 1.07
(c) 1.01
(d) 1.14
B. __________
(e) 1.2
6. Records show that the probability of seeing a hawk migrating on a day in
September is about 35%. What is the minimum number of days a person must
watch to be at least 96.8% sure of seeing one or more hawks migrating?
(a) 5
(b) 6
(c) 7
(d) 8
(e) 9
7. We are interested in when the first 6 will occur for repeated rolls of a
balanced die. What is the population mean for this geometric distribution
(i.e., the expected number of rolls for the first 6 to occur)?
(a) 6
(b) 1
6
(c) 7
6. _____________
(d) 8
7. _____________
(e) 9
8. Rita is studying to be a real estate agent. About 61% of all people who take the
licensing exam pass. Let n = 1, 2, 3, … represent the number of times a person
takes the exam until he or she passes.
A. What is the formula for the probability distribution of the random variable n.
(a) P(n) = (0.61)n(0.39)n1
(b) P(n) = 0.39(0.61)n1
(c) P(n) = 0.61(0.39)n1
(d) P(n) = (0.61)n1(0.39)n
(e) P(n) = (0.39)n
B. What is the probability that Rita will need three attempts to pass the exam?
(a) 0.227
(b) 0.036
(c) 0.145
(d) 0.093
(b) 0.059
(c) 0.152
(d) 0.023
B. __________
(e) 0.059
C. What is the probability that Rita will need more than three attempts to pass
the exam?
(a) 0.941
8. A. __________
C. __________
(e) 0.907
Copyright © Houghton Mifflin Company. All rights reserved.
Part III: Sample Chapter Tests and Answers
CHAPTER 5 TEST
103
FORM C
PAGE 3
9. Suppose that the average number of customers calling a technical support number in a
10-minute period is seven customers. The company wants a probability distribution
for the number of people calling each 10 minutes.
A. What is the formula for the Poisson probability distribution?
7 r
(a) P  r   e 7
7
(b) P  r   e rr !
7
7
(c) P  r   e rr !
7
r
(d) P  r   7 r !
7
r!
9. A. __________
7 r
(e) P  r   e 7
r!
e
B. What is the probability that exactly four customers call the support number
during a 10-minute period?
(a) 0.0912
(b) 0.9088
(c) 0.0521
(d) 0.1729
(e) 0.5714
C. What is the probability that more than four customers call the support number
during a 10-minute period?
(a) 0.1729
(b) 0.8271
(c) 0.0817
(d) 0.9183
B. __________
C. __________
(e) 0.9088
10. The probability that a manufactured part at a plant is defective is 0.02. The
plant has manufactured 300 parts. Let r be the random variable representing
the number of defective parts.
A. What is the formula for the Poisson approximation to the binomial
probability distribution of r?
(a) P  r  
e0.02  300 
r!
r
0.02
0.02r
(c) P  r   e
r!
10. A. __________
6 r
(b) P  r   e 6
r!
6 r
(d) P  r   e 6
r!
6
(e) P  r   e rr !
6
B. What is the probability that exactly five parts are defective?
(a) 0.0268
(b) 0.9732
(c) 0.8394
(d) 0.0000
B. __________
(e) 0.1606
C. What is the probability that fewer than two parts are defective?
(a) 0.0620
(b) 0.9380
(c) 0.9826
Copyright © Houghton Mifflin Company. All rights reserved.
(d) 0.0174
C. __________
(e) 0.9999