Download Ch08 Sect02 Keller MS AISE TB Last modified

CHAPTER 8 SECTION 2: CONTINUOUS PROBABILITY DISTRIBUTIONS
MULTIPLE CHOICE
55. A standard normal distribution is a normal distribution with:
a. a mean of zero and a standard deviation of one.
b. a mean of one and a standard deviation of zero.
c. a mean always larger than the standard deviation.
d. None of these choices.
ANS: A
PTS: 1
REF: SECTION 8.2
56. What proportion of the data from a normal distribution is within two standard deviations from the
mean?
a. 0.3413
b. 0.4772
c. 0.6826
d. 0.9544
ANS: D
PTS: 1
REF: SECTION 8.2
57. Given that Z is a standard normal random variable, the area to the left of a value z is expressed as
a. P(Z  z)
b. P(Z  z)
c. P(0  Z  z)
d. P(Z  z)
ANS: B
PTS: 1
REF: SECTION 8.2
58. If X has a normal distribution with mean 60 and standard deviation 6, which value of X corresponds
with the value z = 1.96?
a. x = 71.76
b. x = 67.96
c. x = 61.96
d. x = 48.24
ANS: A
PTS: 1
REF: SECTION 8.2
59. Which of the following is not a characteristic for a normal distribution?
a. It is symmetrical.
b. The mean is always zero.
c. The mean, median, and mode are all equal.
d. It is a bell-shaped distribution.
ANS: B
PTS: 1
REF: SECTION 8.2
60. Given that Z is a standard normal variable, the variance of Z:
a. is always greater than 2.0.
b. is always greater than 1.0.
c. is always equal to 1.0.
d. cannot assume a specific value.
ANS: C
PTS: 1
REF: SECTION 8.2
This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold,
copied, or distributed without the prior consent of the publisher.
61. Given that Z is a standard normal random variable, a negative value (z) on its distribution would
indicate:
a. z is to the left of the mean.
b. the standard deviation of this Z distribution is negative.
c. the area between zero and the value z is negative.
d. None of these choices.
ANS: A
PTS: 1
REF: SECTION 8.2
62. A larger standard deviation of a normal distribution indicates that the distribution becomes:
a. narrower and more peaked.
b. flatter and wider.
c. more skewed to the right.
d. more skewed to the left.
ANS: B
PTS: 1
REF: SECTION 8.2
63. In its standardized form, the normal distribution:
a. has a mean of 0 and a standard deviation of 1.
b. has a mean of 1 and a variance of 0.
c. has an area equal to 0.5.
d. cannot be used to approximate discrete probability distributions.
ANS: A
PTS: 1
REF: SECTION 8.2
64. Most values of a standard normal distribution lie between:
a. 0 and 1
b. 3 and 3
c. 0 and 3
d. minus infinity and plus infinity
ANS: B
PTS: 1
REF: SECTION 8.2
65. Bob took a math test whose mean was 70 and standard deviation was 5. The total points possible was
100. Bob's results were reported to be at the 95th percentile. What was Bob's actual exam score,
rounded to the nearest whole number?
a. 95
b. 78
c. 75
d. 62
ANS: B
PTS: 1
REF: SECTION 8.2
66. Bob took a statistics test whose mean was 80 and standard deviation was 5. The total points possible
was 100. Bob's score was 2 standard deviations below the mean. What was Bob's score, rounded to the
nearest whole number?
a. 78
b. 70
c. 90
d. None of these choices.
ANS: B
PTS: 1
REF: SECTION 8.2
This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold,
copied, or distributed without the prior consent of the publisher.
67. Bob took a biology exam whose mean was 70 with standard deviation 5. He also took a chemistry
exam whose mean was 80 with standard deviation 10. He scored 85 on both exams. On which exam
did he do better compared to the other students who took the exam?
a. He did better on the biology exam, comparatively speaking.
b. He did better on the chemistry exam, comparatively speaking.
c. He did the same on both exams, relatively speaking.
d. Cannot tell without more information.
ANS: A
PTS: 1
REF: SECTION 8.2
68. Suppose Bob's exam score was at the 80th percentile on an exam whose mean was 90. What was Bob's
exam score?
a. 76.81
b. 72.00
c. 80.00
d. Cannot tell without more information.
ANS: D
PTS: 1
REF: SECTION 8.2
TRUE/FALSE
69. If we standardize the normal curve, we express the original X values in terms of their number of
standard deviations away from the mean.
ANS: T
PTS: 1
REF: SECTION 8.2
70. A normal distribution is symmetric; therefore the probability of being below the mean is 0.50 and the
probability of being above the mean is 0.50.
ANS: T
PTS: 1
REF: SECTION 8.2
71. A random variable X is standardized by subtracting the mean and dividing by the variance.
ANS: F
PTS: 1
REF: SECTION 8.2
72. A random variable X has a normal distribution with mean 132 and variance 36. If x = 120, its
corresponding value of Z is 2.0.
ANS: F
PTS: 1
REF: SECTION 8.2
73. A random variable X has a normal distribution with a mean of 250 and a standard deviation of 50.
Given that X = 175, its corresponding value of Z is 1.50.
ANS: T
PTS: 1
REF: SECTION 8.2
74. Given that Z is a standard normal random variable, a negative value of Z indicates that the standard
deviation of Z is negative.
ANS: F
PTS: 1
REF: SECTION 8.2
75. In the standard normal distribution, z0.05 = 1.645 means that 5% of all values of z are below 1.645 and
95% are above it.
ANS: F
PTS: 1
REF: SECTION 8.2
This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold,
copied, or distributed without the prior consent of the publisher.
76. The probability that a standard normal random variable Z is less than 3.5 is approximately 0.
ANS: T
PTS: 1
REF: SECTION 8.2
77. If the value of Z is z = 99, that means you are at the 99th percentile on the Z distribution.
ANS: F
PTS: 1
REF: SECTION 8.2
78. The 10th percentile of a Z distribution has 10% of the Z-values lying above it.
ANS: F
PTS: 1
REF: SECTION 8.2
79. The probability that Z is less than 2 is the same as one minus the probability that Z is greater than +2.
ANS: F
PTS: 1
REF: SECTION 8.2
80. If your golf score is 3 standard deviations below the mean, its corresponding value on the Z
distribution is 3.
ANS: T
PTS: 1
REF: SECTION 8.2
81. Suppose X has a normal distribution with mean 70 and standard deviation 5. The 50th percentile of X is
70.
ANS: T
PTS: 1
REF: SECTION 8.2
82. A national standardized testing company can tell you your relative standing on an exam without
divulging the mean or the standard deviation of the exam scores.
ANS: T
PTS: 1
REF: SECTION 8.2
COMPLETION
83. Suppose X has a normal distribution with mean 40 and standard deviation 2. Shifting all the X values
to the right 10 units results in a normal distribution with mean ____________________ and standard
deviation ____________________.
ANS:
50; 2
fifty; two
PTS: 1
REF: SECTION 8.2
84. ____________________ the value of  in a normal distribution will make it wider.
ANS: Increasing
PTS: 1
REF: SECTION 8.2
This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold,
copied, or distributed without the prior consent of the publisher.
85. We standardize a random variable by subtracting its ____________________ and dividing by its
____________________.
ANS: mean; standard deviation
PTS: 1
REF: SECTION 8.2
86. Suppose X has a normal distribution with mean 10 and standard deviation 2. The probability that X is
less than 8 is equal to the probability that Z is less than ____________________.
ANS: 1
PTS: 1
REF: SECTION 8.2
87. P(Z > 1.9) = ____________________ P(Z < 1.9).
ANS:
1 

PTS: 1
REF: SECTION 8.2
88. P(1 < Z < 2) = P(Z < 2)  ____________________.
ANS:
P(Z < 1)
P(Z<1)
PTS: 1
REF: SECTION 8.2
89. The mean of the standard normal distribution is ____________________ and the standard deviation is
____________________.
ANS:
0; 1
zero; one
PTS: 1
REF: SECTION 8.2
90. P(Z > 3.00) is approximately ____________________.
ANS:
0
zero
PTS: 1
REF: SECTION 8.2
This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold,
copied, or distributed without the prior consent of the publisher.
91. P(Z < 3.00) is approximately ____________________.
ANS:
1
one
PTS: 1
REF: SECTION 8.2
92. Suppose X is a normal random variable with mean 70 and standard deviation 3. Then P(X = 3) =
____________________.
ANS:
0
zero
PTS: 1
REF: SECTION 8.2
93. Z.025 is the value of Z such that the area to the ____________________ of Z is .9750.
ANS: left
PTS: 1
REF: SECTION 8.2
SHORT ANSWER
Lamps Lifetime
A certain brand of flood lamps has a lifetime that has a normal distribution with a mean of 3,750
hours and a standard deviation of 300 hours.
94. {Lamps Lifetime Narrative} What proportion of these lamps will last for more than 4,000 hours?
ANS:
0.2033
PTS: 1
REF: SECTION 8.2
95. {Lamps Lifetime Narrative} What proportion of these lamps will last less than 3,600 hours?
ANS:
0.3085
PTS: 1
REF: SECTION 8.2
96. {Lamps Lifetime Narrative} What proportion of these lamps will last between 3,800 and 4,100 hours?
ANS:
0.3115
PTS: 1
REF: SECTION 8.2
This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold,
copied, or distributed without the prior consent of the publisher.
97. {Lamps Lifetime Narrative} What lifetime should the manufacturer advertise for these lamps in order
that only 2% of the lamps will burn out before the advertised lifetime?
ANS:
3135
PTS: 1
REF: SECTION 8.2
Diet
Researchers studying the effects of a new diet found that the weight loss over a one-month period by
those on the diet was normally distributed with a mean of 10 pounds and a standard deviation of 5
pounds.
98. {Diet Narrative} What proportion of the dieters lost more than 12 pounds?
ANS:
0.3446
PTS: 1
REF: SECTION 8.2
99. {Diet Narrative} What proportion of the dieters gained weight?
ANS:
0.0028
PTS: 1
REF: SECTION 8.2
100. {Diet Narrative} If a dieter is selected at random, what is the probability that the dieter lost more than
7.5 pounds?
ANS:
0.6915
PTS: 1
REF: SECTION 8.2
101. Let X be a normally distributed random variable with a mean of 12 and a standard deviation of 1.5.
What proportions of the values of X are:
a.
b.
c.
less than 14
more than 8
between 10 and 13
ANS:
a.
b.
c.
0.9082
0.9962
0.6568
PTS: 1
REF: SECTION 8.2
This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold,
copied, or distributed without the prior consent of the publisher.
102. If Z is a standard normal random variable, find the value z for which:
a.
b.
c.
d.
the area between 0 and z is 0.3729
the area to the right of z is 0.7123
the area to the left of z is 0.1736
the area between z and z is 0.6630
ANS:
a.
b.
c.
d.
1.14
.56
.94
0.96
PTS: 1
REF: SECTION 8.2
103. If Z is a standard normal random variable, find the following probabilities:
a.
b.
c.
d.
e.
P(Z  1.77)
P(Z  1.96)
P(0.35  Z  0.85)
P(2.88  Z  2.15)
P(Z  1.45)
ANS:
a.
b.
c.
d.
e.
0.0384
0.9750
0.1655
0.0138
0.9265
PTS: 1
REF: SECTION 8.2
Math Scores
Scores of high school students on a national mathematics exam were normally distributed with a mean
of 86 and a standard deviation of 4. (Total possible points = 100.)
104. {Math Scores Narrative} What is the probability that a randomly selected student will have a score of
80 or higher?
ANS:
0.9332
PTS: 1
REF: SECTION 8.2
105. {Math Scores Narrative} What is the probability that a randomly selected student will have a score
between 80 and 90?
This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold,
copied, or distributed without the prior consent of the publisher.
ANS:
0.7745
PTS: 1
REF: SECTION 8.2
106. {Math Scores Narrative} What is the probability that a randomly selected student will have a score of
94 or lower?
ANS:
0.9772
PTS: 1
REF: SECTION 8.2
Saving Accounts
A bank has determined that the monthly balances of the saving accounts of its customers are normally
distributed with an average balance of $1,200 and a standard deviation of $250.
107. {Saving Accounts Narrative} What proportion of customers have monthly balances less than $1,000?
ANS:
0.2119
PTS: 1
REF: SECTION 8.2
108. {Saving Accounts Narrative} What proportion of customers have monthly balances more than $1,125?
ANS:
0.6179
PTS: 1
REF: SECTION 8.2
109. {Saving Accounts Narrative} What proportion of customers have monthly balances between $950 and
$1,075?
ANS:
0.1498
PTS: 1
REF: SECTION 8.2
CIS Graduate Salary
The recent average starting salary for new college graduates in computer information systems is
$47,500. Assume salaries are normally distributed with a standard deviation of $4,500.
110. {CIS Graduate Salary Narrative} What is the probability of a new graduate receiving a salary between
$45,000 and $50,000?
ANS:
0.4246
PTS: 1
REF: SECTION 8.2
This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold,
copied, or distributed without the prior consent of the publisher.
111. {CIS Graduate Salary Narrative} What is the probability of a new graduate getting a starting salary in
excess of $55,000?
ANS:
0.0475
PTS: 1
REF: SECTION 8.2
112. {CIS Graduate Salary Narrative} What percent of starting salaries are no more than $42,250?
ANS:
12.10%
PTS: 1
REF: SECTION 8.2
113. {CIS Graduate Salary Narrative} What is the cutoff for the bottom 5% of the salaries?
ANS:
$40,097.50
PTS: 1
REF: SECTION 8.2
114. {CIS Graduate Salary Narrative} What is the cutoff for the top 3% of the salaries?
ANS:
$55,960
PTS: 1
REF: SECTION 8.2
115. A worker earns $16 per hour at a plant and is told that only 5% of all workers make a higher wage. If
the wage is assumed to be normally distributed and the standard deviation of wage rates is $5 per hour,
find the average wage for the plant workers per hour.
ANS:
P(X > 16) = .05  (16  ) / 5 = 1.645   = $7.78
PTS: 1
REF: SECTION 8.2
This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold,
copied, or distributed without the prior consent of the publisher.