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Chapter 8
Sampling Methods and the Central Limit Theorem
41. An experiment involves selecting a random sample of 256 middle managers at random for study.
The sample mean of the annual income is computed to be $35,420 and the sample standard deviation is
$2,050. What is the standard error of the mean?
A) $128.125
B) $138.36
C) $2,050
D) $8.01
Answer: A
43. Suppose a research firm conducted a survey to determine the average amount of money steady
smokers spend on cigarettes during a week. A sample of 100 steady smokers revealed that the sample
mean is $20 and the sample standard deviation is $5. What is the probability that a sample of 100 steady
smokers spend between $19 and $21?
A) 0.4772
B) 0.0228
C) 0.9544
D) $20
Answer: C
44. A state highway inspector needs an estimate of the mean weight of trucks. He selects a random
sample of 49 trucks passing the weighing station and finds the mean is 15.8 tons, with a standard
deviation of the sample of 4.2 tons. What is probability that a truck will weigh less than 14.3 tons?
A) 0.0062
B) 0.3632
C) 0.1368
D) 0.4938
Answer: A
Multiple Choice
Use the following to answer questions 68-71:
An accounting firm is planning for the next tax preparation season. From last year's returns, the firm
collects a systematic random sample of 100 filings. The 100 filings showed an average preparation time
of 90 minutes with a standard deviation of 140 minutes.
69. What is the standard error of the mean?
A) 14 minutes
B) 140 minutes
C) 1.4 minutes
D) 90 minutes
Answer: A
70. What is the probability that the mean completion time will be more than 120 minutes?
A) Approximately zero
B) 0.0832
C) 0.4168
D) 0.0162
Answer: D
Statistical Techniques in Business & Economics, Lind/Marchal/Wathen, 13/e 125
71. What is the probability that the mean completion time is between 1 and 2 hours, i.e., 60 and 120
minutes?
A) Approximately 1.
B) 0.1664
C) 0.8336
D) 0.9676
Answer: D
Use the following to answer questions 72-75:
A group of statistics students decided to conduct a survey at their university to find the average (mean)
amount of time students spend studying per week. Based on a simple random sample, they surveyed 144
students. The statistics showed that students studied an average of 20 hours per week with a standard
deviation of 10 hours.
73. What is the probability that a sample mean would exceed 20 hours per week?
A) 1.0
B) 0.5
C) 1.96
D) Cannot be calculated based on the given information.
Answer:
74. What is the probability of finding a sample mean less than 18 hours?
A) 0.4820
B) 0.4920
C) 0.0080
D) 0.0180
Answer: C
75. What is the probability that average student study time is between 18 and 22 hours?
A) 0.9640
B) 0.0160
C) 0.0360
D) 0.9840
Answer: D
Use the following to answer questions 76-79:
The Intelligence Quotient (IQ) test scores are normally distributed with a mean of 100 and a standard
deviation of 15.
78. You enrolled in a class of 25 students. What is the probability that the class' average IQ exceeds
130?
A) 0.0228
B) 0.9772
C) Approximately zero
D) 0.9544
Answer: C
Use the following to answer questions 80-83:
Truck tire life is normally distributed with a mean of 60,000 miles and a standard deviation of 4,000
miles.
126 Test Bank, Chapter 8
80. What is the probability that a tire will last 72,000 miles or more?
A) 0.0013
B) 0.9987
C) 0.4987
D) 0.9544
Answer: A
81. What is the probability that a tire lasts between 54,000 and 66,000 miles?
A) 0.4332
B) 0.8664
C) 1.00
D) very likely
Answer: B
82. You bought four tires. What is the probability that the average mileage of the four tires exceeds
66,000 miles?
A) 0.0013
B) 0.9987
C) 0.4987
D) 0.9544
Answer: A
83. For a set of four tires, what is the probability that the average tire life is between 57,000 and 63,000
miles?
A) 0.4332
B) 0.8664
C) 1.00
D) very likely
Answer: B