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Instructor's Resource Guide Understandable Statistics, 9/e
104
CHAPTER 6 TEST
FORM A
PAGE 1
1. Give the reason each curve is not a normal curve.
(a)
1. (a) __________________________
(b)
(b) _________________________________
2. According to the empirical rule, for a distribution that is
symmetric and bell-shaped, approximately _______ of
the data values will lie within 3 standard deviations on
each side of the mean.
2. ______________________________
3. Assuming that the heights of boys in a high-school basketball tournament are normally distributed with mean 70 inches
and standard deviation 2.5 inches, how many boys in a group
of 40 are expected to be taller than 75 inches?
3. _____________________________
4. Let x be a random variable that represents the length of time
it takes a student to complete Dr. Gill’s chemistry lab project.
From long experience, it is known that x has a normal distribution with mean  = 3.6 hours and standard deviation  = 0.5.
Convert each of the following x intervals to standard z intervals.
(a) x  4.5
4. (a) __________________________
(b) 3  x  4
(b) __________________________
(c) x  2.5
(c) __________________________
Convert each of the following z intervals to raw-score x intervals.
(d) z  1
(d) __________________________
(e) 1  z  2
(e) __________________________
(f) z  1.5
(f) __________________________
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Part III: Sample Chapter Tests and Answers
CHAPTER 6 TEST
105
FORM A
PAGE 2
5. John and Joel are salesmen in different districts. In
John’s district, the long-term mean sales is $17,319
each month with standard deviation $684. In Joel’s
district, the long-term mean sales is $21,971 each
month with standard deviation $495. Assume that
sales in both districts follow a normal distribution.
(a) Last month John sold $19,214 worth of merchandise,
whereas Joel sold $22,718 worth. Relative to the
buying habits of customers in each district, does
this mean that Joel was a better salesman during last
month? Explain.
5. (a) __________________________
(b) Convert Joel’s sales last month to a standard
z score, and do the same for John’s sales last
month. Then locate both z scores under a
standard normal curve. Who do you think was
the better salesman last month? Explain your answer.
(b) __________________________
6. The length of time to complete a door assembly on
an automobile factory assembly line is normally distributed with mean  = 6.7 minutes and standard
deviation  = 2.2 minutes. For a door selected at
random, what is the probability that the assembly-line
time will be
(a) 5 minutes or less?
6. (a) __________________________
(b) 10 minutes or more?
(b) __________________________
(c) between 5 and 10 minutes?
(c) __________________________
7. From long experience, it is known that the time it takes
to do an oil change and lubrication job on a vehicle has
a normal distribution with mean  = 17.8 minutes and
standard deviation  = 5.2 minutes. An auto service shop
will give a free lube job to any customer who must wait
beyond the guaranteed time to complete the work. If the
shop does not want to give more than 1% of its customers
a free lube job, how long should the guarantee be (round
to the nearest minute)?
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7. _____________________________
Instructor's Resource Guide Understandable Statistics, 9/e
106
CHAPTER 6 TEST
FORM A
PAGE 3
8. You are examining a quality-control chart regarding the number
of employees absent each shift from a large manufacturing plant.
The plant is staffed so that operations are still efficient when
the average number of employees absent each shift is  = 15.7
with standard deviation  = 3.5. For the most recent 12 shifts,
the number of absent employees was as follows:
Shift
#
1
6
2
10
3
7
4
16
5
19
6
18
7
17
8
21
9
22
10
18
11
16
12
19
(a) Make a control chart showing the number of employees
absent during the 12-day period.
(b) Are there any periods during which the number absent
is out of control? Identify the out-of-control periods
according to type I, type II, and type III out-of-control
signals.
8. (a)
(b) __________________________
9. Medical treatment will cure about 87% of all people who
suffer from a certain eye disorder. Suppose that a large medical
clinic treats 57 people with this disorder. Let r be a random
variable that represents the number of people who will recover.
The clinic wants a probability distribution for r.
(a) Write a brief but complete description in which you
explain why the normal approximation to the binomial
would apply. Are the assumptions satisfied? Explain.
9. (a) __________________________
(b) Estimate P  r  47  .
(b) __________________________
(c) Estimate P  47  r  55 .
(c) __________________________
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Part III: Sample Chapter Tests and Answers
CHAPTER 6 TEST
107
FORM B
PAGE 1
1. Give the reason each curve is not a normal curve.
(a)
1. (a) __________________________
(b)
(b) __________________________
2. According to the empirical rule, for a distribution that is
symmetric and bell-shaped, approximately _______ of
the data values will lie within 1 standard deviation on
each side of the mean.
2. ______________________________
3. Assuming that the weights of newborn babies at a certain
hospital are normally distributed with mean 6.5 pounds and
standard deviation 1.2, how many babies in a group of 80 from
this hospital are expected to weigh more than 8.9 pounds?
3. _____________________________
4. Let x be a random variable that represents the length of time
it takes a student to write a term paper for Dr. Adam’s
sociology class. After interviewing many students, it was
found that x has an approximately normal distribution with
mean  = 6.8 hours and standard deviation  = 2.1 hours.
Convert each of the following x intervals to standardized z intervals.
(a) x  7.5
4. (a) __________________________
(b) 5  x  8
(b) __________________________
(c) x  4
(c) __________________________
Convert each of the following z intervals to raw-score x intervals.
(d) z  2
(d) __________________________
(e) 0  z  2
(e) __________________________
(f) z  3
(f)_ __________________________
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Instructor's Resource Guide Understandable Statistics, 9/e
108
CHAPTER 6 TEST
FORM B
PAGE 2
5. Operating temperatures of two models of portable
electric generators follow a normal distribution.
For generator I, the mean temperature is 1 = 148F
with standard deviation 1 = 25F. For generator II,
the mean temperature is 2 = 143F with standard
deviation 2 = 8F. At peak power demand, generator I was operating at 166F, and generator II was
operating at 165F.
(a) At peak power output, both generators are operating at about the same temperature. Relative
to the operating characteristics, is one a lot
hotter than the other? Explain.
5. (a) __________________________
(b) Convert the peak power temperature for each
generator to standard z units. Then locate both
z scores under a standard normal curve. Could
one generator be near a meltdown? Which one?
Explain your answer.
(b) __________________________
6. Weights of a certain model of fully loaded gravel
truck follow a normal distribution with mean
 = 6.4 tons and standard deviation  = 0.3 ton.
What is the probability that a fully loaded truck
of this model is
(a) less than 6 tons?
6. (a) __________________________
(b) more than 7 tons?
(b) __________________________
(c) between 6 and 7 tons?
(c) __________________________
7. Quality-control studies for Speedy Jet computer printers
show that the lifetime of the printer follows a normal distribution
with mean  = 4 years and standard deviation  = 0.78 years.
The company will replace any printer that fails during the
guarantee period. How long should Speedy Jet printers be
guaranteed if the company wishes to replace no more than 10%
of the printers?
7. _____________________________
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Part III: Sample Chapter Tests and Answers
CHAPTER 6 TEST
109
FORM B
PAGE 3
8. A toll-free computer software support service for a spreadsheet program has established a target length of time for each
customer help phone call. The calls are targeted to have a mean
duration of 12 minutes with a standard deviation 3 minutes. For
one help technician, the most recent 10 calls had the following
durations:
Call #
Length
1
15
2
25
3
10
4
9
5
20
6
19
7
11
8
5
9
4
10
8
(a) Make a control chart showing the number of calls.
(b) Are there any periods during which the lengths of
calls are out of control? Identify the out-of-control
periods according to type I, type II, and type III out-ofcontrol signals.
8. (a)
(b) __________________________
9. Psychology 231 can be taken as an online course on
a pass/fail basis. Long experience with this course shows
that about 71% of the students pass. This semester, 88
students are taking Psychology 231 online. Let r be a random
variable that represents the number that will pass. The
psychology department wants a probability distribution for r.
(a) Write a brief but complete description in which you
explain why the normal approximation to the binomial
would apply. Are the assumptions satisfied? Explain.
9. (a) __________________________
(b) Estimate P  r  60 .
(b) __________________________
(c) Estimate P  60  r  70 .
(c) __________________________
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Instructor's Resource Guide Understandable Statistics, 9/e
110
CHAPTER 6 TEST
FORM C
PAGE 1
Write the letter of the response that best answers each problem.
1. Which of the following curves is a normal curve?
(a)
(b)
(c)
(d)
1. __________
(e)
2. According to the empirical rule, for a distribution that is symmetric and bell-shaped
(in particular, for a normal distribution), approximately _______ of the data values will
lie within 2 standard deviations on each side of the mean.
(a) 75%
(b) 95%
(c) 68%
(d) 88.9%
(e) 99.7%
3. The delivery time for a package sent within the United States is normally distributed
with mean of 4 days and standard deviation of approximately 1 day. If 300 packages
are being sent, how many packages do we expect to arrive in less than 3 days?
(a) 8
(b) 96
(c) 102
(d) 198
2. __________
3. __________
(e) 48
4. Let x be a random variable that represents the length of time it takes a student to complete a take-home exam in Dr. Larson’s psychology class. After interviewing many
students, it was found that x has an approximately normal distribution with mean
 = 5.2 hours and standard deviation  = 1.8 hours.
A. Convert the x interval x  9.7 to a standard z interval.
(a) z  2.5
(b) z  2.5
(c) z  4.5
(d) z  2.5
4. A. __________
(e) z  2.5
B. Convert the z interval –1.5  z  1 to a raw-score x interval.
(a) 2.5  x  7
(b) 3.44  x  6.66
(c) 3.7  x  12.2
(d) 7  x  2.5
B. __________
(e) –3.7 ≤ x ≤ –2.3
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Part III: Sample Chapter Tests and Answers
CHAPTER 6 TEST
111
FORM C
PAGE 2
5. Maria and Zoe are taking Biology 105 but are in different classes. Maria’s
class has an average of 78% with a standard deviation of 5% on the midterm,
whereas Zoe’s class has an average of 83% with a standard deviation of 12%.
Assume that scores in both classes follow a normal distribution.
A. Convert Maria’s midterm score of 84 to a standard z score.
(a) 0.083
(b) 0.5
(c) 0.2
(d) 1.2
5. A. __________
(e) 6
B. Convert Zoe’s midterm score of 89 to a standard z score.
(a) 1.2
(b) 0.5
(c) 6
(d) 0.917
B. __________
(e) 2.2
C. Who did better relative to her class?
C. __________
(a) Maria
(b) Zoe
(c) They performed the same.
(d) Neither
(e) Cannot determine
6. The lifetime of a SuperTough AAA battery is normally distributed with
mean  = 28.5 hours and standard deviation  = 5.3 hours. For a battery
selected at random, what is the probability that the lifetime will be
A. 25 hours or less?
(a) 0.7454
6. A. __________
(b) 0.6604
(c) 0.2546
(d) 0.3396
(e) 0.9999
B. 34 hours or more?
(a) 0.8485
(b) 0.1515
B. __________
(c) 1.038
(d) 0.8508
(e) 0.1492
C. between 25 and 34 hours?
(a) 0.4038
(b) 0.5962
C. __________
(c) 0.1054
(d) 0.8946
(e) 0.2736
7. Quality-control studies for Dependable Dishwashers show that the lifetime of a
dishwasher follows a normal distribution with mean  = 8 years and standard
deviation  = 1.2 years. The company will replace any dishwasher that fails
during the guarantee period. How long should the company’s dishwashers
be guaranteed if the company wishes to replace no more than 2% of the dishwashers?
(a) 0.16 year
(b) 0.13 year
(c) 5.5 years
(d) 10.5 years
(e) 2.5 years
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7. __________
Instructor's Resource Guide Understandable Statistics, 9/e
112
CHAPTER 6 TEST
FORM C
PAGE 3
8. When evaluating a control chart, which of the following is not a warning
signal that a random variable x is out of control?
8. __________
(a) A run of nine consecutive points on one side of the center line
(the line at target value ).
(b) One point falls beyond the 3 level.
(c) Two points fall beyond the 3 level.
(d) At least two points lie beyond the 2 level on the same side of the center line.
(e) At least two of three consecutive points lie beyond the 2  level on the same side of the
center line.
9. Records show that 29% of all payments to a mail-order company are submitted
after the due date. Suppose that 50 payments are submitted this week. Let r be a
random variable that represents the number of payments that are late. Use the
normal approximation to the binomial to estimate
A. P(r  20)
(a) 0.0307
9. A. __________
(b) 0.0594
(c) 0.9406
(d) 0.9564
(e) 0.0436
B. P(20  r  25)
(a) 0.0591
B. __________
(b) 0.0585
(c) 0.0431
(d) 0.0304
(e) 0.0298
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