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Module 6 Test
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers
the question.
Provide an appropriate response.
1) The area under the standard normal curve between 1 and 2 is equal to 0.1359. Scores on a particular
aptitude test are normally distributed with a mean of 100 and a standard deviation of 10. Which of the
following are equal to 13.59%?
a. The percentage of scores between 120 and 130
b. The percentage of scores between 110 and 120
c. The percentage of scores between 80 and 90
d. The percentage of scores between 90 and 120
e. The percentage of scores between 90 and 110
A) a, b
B) b
C) e
D) b, c
Answer: D
Objective: (6.1) *Know Concepts: Normally Distributed Variables
2) Which of the variables below do you think will be roughly normally distributed?
a. Weights of 10 year old boys
b. Incomes of 40 year old adults
c. The numbers that show up when you roll a balanced die
d. The amount of coffee which a filling machine puts into "4 ounce jars"
A) a, b, d
B) a and d
C) a, b, c, d
Answer: B
Objective: (6.1) *Know Concepts: Normally Distributed Variables
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D) a only
Solve the problem.
3) Frequency data were reported for the ages of full-time employees at a company. The age distribution is
given in the table. Obtain a relative-frequency histogram of these data and determine whether the ages are
approximately normally distributed.
Age
(yrs)
20
25
30
35
40
45
50
55
60
Frequency
25
30
35
40
45
50
55
60
65
5
60
443
340
231
75
87
35
15
A) Yes. The distribution is bell-shaped.
C) No. The distribution is right-skewed.
B) No. The distribution is left-skewed.
D) No. The distribution is uniform.
Answer: C
Objective: (6.1) Construct Histogram to Determine If Data is Normally Distributed
4) Data were reported for household size (number of people in household) in a small community. The size
distribution is given in the table. Obtain a relative-frequency histogram for these data and determine
whether the household sizes are approximately normally distributed.
Size
Frequency
(# of people)
1
2
3
4
5
6
2
3
4
5
6
7
2
11
35
41
7
3
A) Yes. The distribution is bell-shaped.
C) No. The distribution is right-skewed.
B) No. The distribution is left-skewed.
D) No. The distribution is uniform.
Answer: A
Objective: (6.1) Construct Histogram to Determine If Data is Normally Distributed
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5) A northeastern college has an enrollment of 2835 female students. Records show that the mean height of
these students is 65.2 inches and that the standard deviation is 2.8 inches. The table shows frequency and
relative-frequency data for these heights. If you assume that the distribution of heights is approximately
normal, then you can use the table to estimate areas under the associated normal curve (that is, under the
normal curve that has parameters µ = 65.2 and σ = 2.8). Making this assumption, estimate the area under
the associated normal curve between 62 and 67.
Height
(inches)
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
Freq.
Relative
freq.
16
25
56
96
178
263
322
388
406
361
292
201
113
75
25
16
2
0.0056
0.0088
0.0198
0.0339
0.0628
0.0928
0.1136
0.1369
0.1432
0.1273
0.1030
0.0709
0.0399
0.0265
0.0088
0.0056
0.0007
A) 0.7168
B) 0.6138
C) 0.6766
D) 0.2201
Answer: B
Objective: (6.1) Approximate Area Under Normal Curve
Use a table of areas to obtain the shaded area under the standard normal curve.
6)
-1.76
A) 0.6212
-0.88
0.88
1.76
z
B) 0.8106
C) 0.1894
Answer: D
Objective: (6.2) Find Area Under Standard Normal Curve Given Graph
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D) 0.3788
Use a table of areas to find the specified area under the standard normal curve.
7) The area that lies between 0 and 3.01
A) 0.4987
B) 0.5013
C) 0.9987
D) 0.1217
Answer: A
Objective: (6.2) Find Area Under Standard Normal Curve
Use a table of areas to obtain the shaded area under the standard normal curve.
8)
-2.23
z
2.23
A) 0.9871
B) 0.9742
C) 0.0129
D) 0.0258
Answer: D
Objective: (6.2) Find Area Under Standard Normal Curve Given Graph
Use a table of areas to find the specified area under the standard normal curve.
9) The area that lies between -0.73 and 2.27
A) 0.7557
B) 0.4884
C) 1.54
D) 0.2211
Answer: A
Objective: (6.2) Find Area Under Standard Normal Curve
Use a table of areas for the standard normal curve to find the required z-score.
10) Find z
.
0.45
A) 0.6736
B) 0.3264
C) 0.13
D) -0.13
Answer: C
Objective: (6.2) Find z-Score Given Area
Use a table of areas to obtain the shaded area under the standard normal curve.
11)
-1.88
A) 0.9699
1.88
z
B) 0.0602
C) 0.9398
Answer: C
Objective: (6.2) Find Area Under Standard Normal Curve Given Graph
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D) 0.0301
Use the empirical rule to solve the problem.
12) The amount of Jen's monthly phone bill is normally distributed with a mean of $53 and a standard
deviation of $10. What percentage of her phone bills are between $23 and $83?
A) 68.26%
B) 99.74%
C) 95.44%
D) 99.99%
Answer: B
Objective: (6.3) Use Empirical Rule
13) The annual precipitation for one city is normally distributed with a mean of 326 inches and a standard
deviation of 2.8 inches. Fill in the blanks.
In 95.44% of the years, the precipitation in this city is between ___ and ___ inches.
A) 320.4, 331.6
B) 326, 331.6
C) 317.6, 326
D) 317.6, 334.4
Answer: A
Objective: (6.3) Use Empirical Rule
14) At one college, GPAs are normally distributed with a mean of 3.1 and a standard deviation of 0.4. What
percentage of students at the college have a GPA between 2.7 and 3.5?
A) 95.44%
B) 99.74%
C) 84.13%
D) 68.26%
Answer: D
Objective: (6.3) Use Empirical Rule
Find the specified percentile, quartile, or decile.
15) The annual precipitation for one city is normally distributed with a mean of 25.2 inches and a standard
deviation of 3 inches. Find the 2nd decile.
A) 27.72 inches
B) 19.05 inches
C) 22.68 inches
D) 31.35 inches
Answer: C
Objective: (6.3) Find Percentile/Quartile/Decile
16) The lifetimes of lightbulbs of a particular type are normally distributed with a mean of 266 hours and a
standard deviation of 9 hours. Find the first quartile, Q .
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A) 268.25
B) 263.75
C) 272.03
D) 259.97
Answer: D
Objective: (6.3) Find Percentile/Quartile/Decile
Find the indicated probability or percentage for the normally distributed variable.
17) The variable X is normally distributed.The mean is µ = 22.0 and the standard deviation is σ = 2.4.
Find P(19.7 < X < 25.3).
A) 0.7477
B) 0.3370
C) 0.4107
D) 1.0847
Answer: A
Objective: (6.3) Find Percentage/Probability for Normal Variable
18) A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200
and a standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is
between 200 and 275.
A) 0.9332
B) 0.5
C) 0.0668
D) 0.4332
Answer: D
Objective: (6.3) Find Percentage/Probability for Normal Variable
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Provide an appropriate response.
19) True or false, areas under the standard normal curve cannot be negative, whereas z-scores can be positive
or negative.
A) True
B) False
Answer: A
Objective: (6.3) *Know Concepts: Normally Distributed Variables
20) True or false, the mean of a normally distributed variable can be any real number.
A) True
B) False
Answer: A
Objective: (6.3) *Know Concepts: Normally Distributed Variables
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