Mas202 chapter 7

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1. 1. Sampling distributions describe the distribution of b

a) parameters.
b) statistics.
c) both parameters and statistics.
d) neither parameters nor statistics.

2. 2. The standard error of the mean d

a) is never larger than the standard deviation of the
population.
b) decreases as the sample size increases.
c) measures the variability of the mean from sample
to sample.
d) All of the above.

3. 3. The Central Limit Theorem is important in statistics c

because
a) for a large n, it says the population is approximately
normal.
b) for any population, it says the sampling distribution
of the sample mean is approximately normal, regard-
less of the sample size.
c) for a large n, it says the sampling distribution of the
sample mean is approximately normal, regardless of
the shape of the population.
d) for any sized sample, it says the sampling distribu-
tion of the sample mean is approximately normal.

4. 4. If the expected value of a sample statistic is equal a

to the parameter it is estimating, then we call that
sample statistic
a) unbiased.
b) minimum variance.
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c) biased.
d) random.

5. 5. For air travelers, one of the biggest complaints is c

of the waiting time between when the airplane taxis
away from the terminal until the flight takes off. This
waiting time is known to have a right skewed distribu-
tion with a mean of 10 minutes and a standard devia-
tion of 8 minutes. Suppose 100 flights have been ran-
domly sampled. Describe the sampling distribution of
the mean waiting time between when the airplane
taxis away from the terminal until the flight takes off
for these 100 flights.
a) Distribution is right skewed with mean = 10 minutes
and standard error = 0.8 minutes.
b) Distribution is right skewed with mean = 10 minutes
and standard error = 8 minutes.
c) Distribution is approximately normal with mean =
10 minutes and standard error = 0.8 minutes.
d) Distribution is approximately normal with mean =
10 minutes and standard error = 8 minutes.

6. 6. Which of the following statements about the sam- d

pling distribution of the sample mean is incorrect?
a) The sampling distribution of the sample mean is
approximately normal whenever the sample size is
sufficiently large (n e30 ).
b) The sampling distribution of the sample mean is
generated by repeatedly taking samples of size n and
computing the sample means.
c) The mean of the sampling distribution of the sam-
ple mean is equal to μ .
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d) The standard deviation of the sampling distribution

of the sample mean is equal to σ .

7. 7. Which of the following is true about the sampling a

distribution of the sample mean?
a) The mean of the sampling distribution is always μ .
b) The standard deviation of the sampling distribution
is always σ .
c) The shape of the sampling distribution is always
approximately normal.
d) All of the above are true.

8. 8. True or False: The amount of time it takes to com- T

plete an examination has a left skewed distribution
with a mean of 65 minutes and a standard deviation
of 8 minutes. If 64 students were randomly sampled,
the probability that the sample mean of the sampled
students exceeds 71 minutes is approximately 0.

9. 9. Suppose the ages of students in Statistics 101 follow b

a right skewed distribution with a mean of 23 years
and a standard deviation of 3 years. If we randomly
sampled 100 students, which of the following state-
ments about the sampling distribution of the sample
mean age is incorrect?
a) The mean of the sampling distribution is equal to 23
years.
b) The standard deviation of the sampling distribution
is equal to 3 years.
c) The shape of the sampling distribution is approxi-
mately normal.

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d) The standard error of the sampling distribution is

equal to 0.3 years.

10. 10. Why is the Central Limit Theorem so important to d

the study of sampling distributions?
a) It allows us to disregard the size of the sample
selected when the population is not normal.
b) It allows us to disregard the shape of the sampling
distribution when the size of the population is large.
c) It allows us to disregard the size of the population
we are sampling from.
d) It allows us to disregard the shape of the population
when n is large.

11. 11. A sample that does not provide a good represen- biased
tation of the population from which it was collected is
referred to as a(n)________ sample.

12. 12. True or False: The Central Limit Theorem is con- T

sidered powerful in statistics because it works for any
population distribution provided the sample size is suf-
ficiently large and the population mean and standard
deviation are known.

13. 13. Suppose a sample of n = 50 items is selected a

from a population of manufactured products and the
weight, X, of each item is recorded. Prior experience
has shown that the weight has a probability distribu-
tion with μ = 6 ounces and σ = 2.5 ounces. Which of
the following is true about the sampling distribution
of the sample mean if a sample of size 15 is selected?
a) The mean of the sampling distribution is 6 ounces.
b) The standard deviation of the sampling distribution
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is 2.5 ounces.
c) The shape of the sampling distribution is approxi-
mately normal.
d) All of the above are correct.

14. 14. The mean score of all pro golfers for a particular 0.0228
course has a mean of 70 and a standard deviation of
3.0. Suppose 36 pro golfers played the course today.
Find the probability that the mean score of the 36 pro
golfers exceeded 71.

15. 15. The distribution of the number of loaves of bread Approximately 0

sold per week by a large bakery over the past 5 years
has a mean of 7,750 and a standard deviation of 145
loaves. Suppose a random sample of n = 40 weeks has
been selected. What is the approximate probability
that the mean number of loaves sold in the sampled
weeks exceeds 7,895 loaves?

16. 16. Sales prices of baseball cards from the 1960s are b
known to possess a right skewed distribution with a
mean sale price of $5.25 and a standard deviation of
$2.80. Suppose a random sample of 100 cards from
the 1960s is selected. Describe the sampling distrib-
ution for the sample mean sale price of the selected
cards.
a) Right skewed with a mean of $5.25 and a standard
error of $2.80
b) Normal with a mean of $5.25 and a standard error
of $0.28
c) Right skewed with a mean of $5.25 and a standard
error of $0.28

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d) Normal with a mean of $5.25 and a standard error

of $2.80

17. 17. Major league baseball salaries averaged $3.26 mil- b

lion with a standard deviation of $1.2 million in a cer-
tain year in the past. Suppose a sample of 100 major
league players was taken. What was the standard er-
ror for the sample mean salary?
a) $0.012 million
b) $0.12 million
c) $12 million
d) $1,200.0 million

18. 18. Major league baseball salaries averaged $3.26 b

million with a standard deviation of $1.2 million in
a certain year in the past. Suppose a sample of 100
major league players was taken. Find the approximate
probability that the mean salary of the 100 players
exceeded $3.5 million.
a) Approximately 0
b) 0.0228
c) 0.9772
d) Approximately 1

19. 19. Major league baseball salaries averaged $3.26 a

million with a standard deviation of $1.2 million in
a certain year in the past. Suppose a sample of 100
major league players was taken. Find the approximate
probability that the mean salary of the 100 players
exceeded $4.0 million.
a) Approximately 0
b) 0.0228

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c) 0.9772
d) Approximately 1

20. 20. Major league baseball salaries averaged $3.26 b

million with a standard deviation of $1.2 million in
a certain year in the past. Suppose a sample of 100
major league players was taken. Find the approximate
probability that the mean salary of the 100 players
was no more than $3.0 million.
a) Approximately 0
b) 0.0151
c) 0.9849
d) Approximately 1

21. 21. Major league baseball salaries averaged $3.26 a

million with a standard deviation of $1.2 million in
a certain year in the past. Suppose a sample of 100
major league players was taken. Find the approximate
probability that the mean salary of the 100 players
was less than $2.5 million.
a) Approximately 0
b) 0.0151
c) 0.9849
d) Approximately 1

22. 22. At a computer manufacturing company, the actual a

size of a particular type of computer chips is normally
distributed with a mean of 1 centimeter and a stan-
dard deviation of 0.1 centimeter. A random sample of
12 computer chips is taken. What is the standard error
for the sample mean?
a) 0.029

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b) 0.050
c) 0.091
d) 0.120

23. 23. At a computer manufacturing company, the actual 0.2710 using Excel or
size of a particular type of computer chips is normally 0.2736 using Table E.2
distributed with a mean of 1 centimeter and a stan-
dard deviation of 0.1 centimeter. A random sample of
12 computer chips is taken. What is the probability
that the sample mean will be between 0.99 and 1.01
centimeters?

24. 24. At a computer manufacturing company, the actual 0.0416 using Excel or
size of a particular type of computer chips is normally 0.0418 using Table E.2
distributed with a mean of 1 centimeter and a stan-
dard deviation of 0.1 centimeter. A random sample of
12 computer chips is taken. What is the probability
that the sample mean will be below 0.95 centimeters?

25. 25. At a computer manufacturing company, the actual 1.057

size of a particular type of computer chips is normally
distributed with a mean of 1 centimeter and a stan-
dard deviation of 0.1 centimeter. A random sample of
12 computer chips is taken. Above what value do 2.5%
of the sample means fall?

26. 26. The owner of a fish market has an assistant who c

has determined that the weights of catfish are nor-
mally distributed, with mean of 3.2 pounds and stan-
dard deviation of 0.8 pound. If a sample of 16 fish
is taken, what would the standard error of the mean
weight equal?
a) 0.003
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b) 0.050
c) 0.200
d) 0.800

27. 27. The owner of a fish market has an assistant who b

has determined that the weights of catfish are nor-
mally distributed, with mean of 3.2 pounds and stan-
dard deviation of 0.8 pound. If a sample of 25 fish
yields a mean of 3.6 pounds, what is the Z-score for
this observation?
a) 18.750
b) 2.500
c) 1.875
d) 0.750

28. 28. The owner of a fish market has an assistant who c

has determined that the weights of catfish are nor-
mally distributed, with mean of 3.2 pounds and stan-
dard deviation of 0.8 pound. If a sample of 64 fish
yields a mean of 3.4 pounds, what is probability of
obtaining a sample mean this large or larger?
a) 0.0001
b) 0.0013
c) 0.0228
d) 0.4987

29. 29. The owner of a fish market has an assistant who b

has determined that the weights of catfish are nor-
mally distributed, with mean of 3.2 pounds and stan-
dard deviation of 0.8 pound. What percentage of sam-
ples of 4 fish will have sample means between 3.0 and
4.0 pounds?

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a) 84%
b) 67%
c) 29%
d) 16%

30. 30. For sample size 16, the sampling distribution of b

the mean will be approximately normally distributed
a) regardless of the shape of the population.
b) if the shape of the population is symmetrical.
c) if the sample standard deviation is known.
d) if the sample is normally distributed.

31. 31. The standard error of the mean for a sample of 100 b
is 30. In order to cut the standard error of the mean
to 15, we would
a) increase the sample size to 200.
b) increase the sample size to 400.
c) decrease the sample size to 50.
d) decrease the sample to 25.

32. 32. Which of the following is true regarding the sam- d

pling distribution of the mean for a large sample size?
a) It has the same shape, mean, and standard devia-
tion as the population.
b) It has a normal distribution with the same mean
and standard deviation as the population.
c) It has the same shape and mean as the population,
but has a smaller standard deviation.
d) It has a normal distribution with the same mean as
the population but with a smaller standard deviation.

33. 33. For sample sizes greater than 30, the sampling dis- a
tribution of the mean will be approximately normally
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distributed
a) regardless of the shape of the population.
b) only if the shape of the population is symmetrical.
c) only if the standard deviation of the samples are
known.
d) only if the population is normally distributed.

34. 34. For sample size 1, the sampling distribution of the d

mean will be normally distributed
a) regardless of the shape of the population.
b) only if the shape of the population is symmetrical.
c) only if the population values are positive.
d) only if the population is normally distributed.

35. 35. The standard error of the population proportion b

will become larger
a) as population proportion approaches 0.
b) as population proportion approaches 0.50.
c) as population proportion approaches 1.00.
d) as the sample size increases.

36. 36. True or False: As the sample size increases, the F

standard error of the mean increases.

37. 37. True or False: If the population distribution is sym- T

metric, the sampling distribution of the mean can be
approximated by the normal distribution if the sam-
ples contain 15 observations.

38. 38. True or False: If the population distribution is un- T

known, in most cases the sampling distribution of the
mean can be approximated by the normal distribution
if the samples contain at least 30 observations.
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39. 39. True or False: If the amount of gasoline purchased F

per car at a large service station has a population
mean of 15 gallons and a population standard devia-
tion of 4 gallons, then 99.73% of all cars will purchase
between 3 and 27 gallons.

40. 40. True or False: If the amount of gasoline purchased F

per car at a large service station has a population
mean of 15 gallons and a population standard devi-
ation of 4 gallons and a random sample of 4 cars is
selected, there is approximately a 68.26% chance that
the sample mean will be between 13 and 17 gallons.

41. 41. True or False: If the amount of gasoline purchased T

per car at a large service station has a population
mean of 15 gallons and a population standard devi-
ation of 4 gallons and it is assumed that the amount
of gasoline purchased per car is symmetric, there is
approximately a 68.26% chance that a random sample
of 16 cars will have a sample mean between 14 and 16
gallons.

42. 42. True or False: If the amount of gasoline purchased T

per car at a large service station has a population
mean of 15 gallons and a population standard devi-
ation of 4 gallons and a random sample of 64 cars is
selected, there is approximately a 95.44% chance that
the sample mean will be between 14 and 16 gallons.

43. 43. True or False: As the sample size increases, the T

effect of an extreme value on the sample mean be-
comes smaller.
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44. 44. True or False: If the population distribution is T

skewed, in most cases the sampling distribution of the
mean can be approximated by the normal distribution
if the samples contain at least 30 observations.

45. 45. True or False: A sampling distribution is a distrib- T

ution for a statistic.

46. 46. True or False: Suppose μ = 50 and σ = 10 for a T

population. In a sample where n = 100 is randomly tak-
en, 95% of all possible sample means will fall between
48.04 and 51.96.

47. 47. True or False: Suppose μ = 80 and σ = 20 for a T

population. In a sample where n = 100 is randomly
taken, 95% of all possible sample means will fall above
76.71.

48. 48. True or False: Suppose μ = 50 and σ = 10 for a pop- F

ulation. In a sample where n = 100 is randomly taken,
90% of all possible sample means will fall between 49
and 51.

49. 49. True or False: The Central Limit Theorem ensures T

that the sampling distribution of the sample mean
approaches a normal distribution as the sample size
increases.

50. 50. True or False: The standard error of the mean is T

also known as the standard deviation of the sampling
distribution of the sample mean.

51. F
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51. True or False: A sampling distribution is defined

as the probability distribution of possible sample sizes
that can be observed from a given population.

52. 52. True or False: As the size of the sample is in- F

creased, the standard deviation of the sampling distri-
bution of the sample mean for a normally distributed
population will stay the same.

53. 53. True or False: For distributions such as the normal T

distribution, the arithmetic mean is considered more
stable from sample to sample than other measures of
central tendency.

54. 54. True or False: The fact that the sample means T
are less variable than the population data can be ob-
served from the standard error of the mean.

55. 55. The amount of tea leaves in a can from a particular 0.9545 using Excel or
production line is normally distributed with μ = 110 0.9544 using Table E.2
grams and σ = 25 grams. A sample of 25 cans is to be
selected. What is the probability that the sample mean
will be between 100 and 120 grams?

56. 56. The amount of tea leaves in a can from a particular 0.0228
production line is normally distributed with μ = 110
grams and σ = 25 grams. A sample of 25 cans is to be
selected. What is the probability that the sample mean
will be less than 100 grams?

57. 57. The amount of tea leaves in a can from a particular 0.9772
production line is normally distributed with μ = 110
grams and σ = 25 grams. A sample of 25 cans is to be
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selected. What is the probability that the sample mean

will be greater than 100 grams?

58. 58. The amount of tea leaves in a can from a particular 101.7757
production line is normally distributed with μ = 110
grams and σ = 25 grams. A sample of 25 cans is to be
selected. So, 95% of all sample means will be greater
than how many grams?

59. 59. The amount of tea leaves in a can from a particular 104.8 and 115.2
production line is normally distributed with μ = 110
grams and σ = 25 grams. A sample of 25 cans is to be
selected. So, the middle 70% of all sample means will
fall between what two values?

60. 60. The amount of time required for an oil and filter 2.5 minutes
change on an automobile is normally distributed with
a mean of 45 minutes and a standard deviation of 10
minutes. A random sample of 16 cars is selected. What
is the standard error of the mean?

61. 61. The amount of time required for an oil and filter 0.4974
change on an automobile is normally distributed with
a mean of 45 minutes and a standard deviation of 10
minutes. A random sample of 16 cars is selected. What
is the probability that the sample mean is between 45
and 52
minutes?

62. 62. The amount of time required for an oil and filter 0.8767
change on an automobile is normally distributed with
a mean of 45 minutes and a standard deviation of
10 minutes. A random sample of 16 cars is selected.
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What is the probability that the sample mean will be

between 39 and 48 minutes?

63. 63. The amount of time required for an oil and filter 40.1 and 49.9 minutes
change on an automobile is normally distributed with
a mean of 45 minutes and a standard deviation of 10
minutes. A random sample of 16 cars is selected. 95%
of all sample means will fall between what two values?

64. 64. The amount of time required for an oil and filter 41.8 minutes
change on an automobile is normally distributed with
a mean of 45 minutes and a standard deviation of 10
minutes. A random sample of 16 cars is selected. 90%
of the sample means will be greater than what value?

65. 65. True or False: The amount of bleach a machine T

pours into bottles has a mean of 36 oz. with a standard
deviation of 0.15 oz. Suppose we take a random sam-
ple of 36 bottles filled by this machine. The sampling
distribution of the sample mean has a mean of 36 oz.

66. 66. True or False: The amount of bleach a machine F

pours into bottles has a mean of 36 oz. with a standard
deviation of 0.15 oz. Suppose we take a random sam-
ple of 36 bottles filled by this machine. The sampling
distribution of the sample mean has a standard error
of 0.15.

67. 67. True or False: The amount of bleach a machine F

pours into bottles has a mean of 36 oz. with a standard
deviation of 0.15 oz. Suppose we take a random sam-
ple of 36 bottles filled by this machine. The sampling

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distribution of the sample mean will be approximately

normal only if the population sampled is normal.

68. 68. The amount of bleach a machine pours into bottles 0.3446
has a mean of 36 oz. with a standard deviation of 0.15
oz. Suppose we take a random sample of 36 bottles
filled by this machine. The probability that the mean
of the sample exceeds 36.01 oz. is __________.

69. 69. The amount of bleach a machine pours into bottles 0.8849
has a mean of 36 oz. with a standard deviation of 0.15
oz. Suppose we take a random sample of 36 bottles
filled by this machine. The probability that the mean
of the sample is less than 36.03 is __________.

70. 70. The amount of bleach a machine pours into bot- 0.9836
tles has a mean of 36 oz. with a standard deviation
of 0.15 oz. Suppose we take a random sample of 36
bottles filled by this machine. The probability that the
mean of the sample is between 35.94 and 36.06 oz. is
__________.

71. 71. The amount of bleach a machine pours into bot- 0.1891
tles has a mean of 36 oz. with a standard deviation
of 0.15 oz. Suppose we take a random sample of 36
bottles filled by this machine. The probability that the
mean of the sample is between 35.95 and 35.98 oz. is
__________.

72. 72. The amount of bleach a machine pours into bot- 35.951 and 36.049 ounces
tles has a mean of 36 oz. with a standard deviation
of 0.15 oz. Suppose we take a random sample of 36
bottles filled by this machine. So, the middle 95% of
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the sample means based on samples of size 36 will be

between __________and __________.

73. 73. A manufacturer of power tools claims that the 80

mean amount of time required to assemble their
top-of-the-line table saw is 80 minutes with a standard
deviation of 40 minutes. Suppose a random sample
of 64 purchasers of this table saw is taken. The mean
of the sampling distribution of the sample mean is
__________ minutes.

74. 74. A manufacturer of power tools claims that the 5

mean amount of time required to assemble their
top-of-the-line table saw is 80 minutes with a standard
deviation of 40 minutes. Suppose a random sample of
64 purchasers of this table saw is taken. The standard
deviation of the sampling distribution of the sample
mean is __________ minutes.

75. 75. A manufacturer of power tools claims that the 0.6554

mean amount of time required to assemble their
top-of-the-line table saw is 80 minutes with a standard
deviation of 40 minutes. Suppose a random sample of
64 purchasers of this table saw is taken. The probabil-
ity that the sample mean will be less than 82 minutes
is __________.

76. 76. A manufacturer of power tools claims that the 0.6898

mean amount of time required to assemble their
top-of-the-line table saw is 80 minutes with a standard
deviation of 40 minutes. Suppose a random sample of
64 purchasers of this table saw is taken. The probabil-

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ity that the sample mean will be between 77 and 89

minutes is __________.

77. 77. A manufacturer of power tools claims that the 0.0548

mean amount of time required to assemble their
top-of-the-line table saw is 80 minutes with a standard
deviation of 40 minutes. Suppose a random sample
of 64 purchasers of this table saw is taken. The prob-
ability that the sample mean will be greater than 88
minutes is __________.

78. 78. A manufacturer of power tools claims that the 70.2 and 89.8 minutes
mean amount of time required to assemble their
top-of-the-line table saw is 80 minutes with a standard
deviation of 40 minutes. Suppose a random sample of
64 purchasers of this table saw is taken. So, the middle
95% of the sample means based on samples of size 64
will be between __________ and __________.

79. 79. To use the normal distribution to approximate the nπ and n(1− π )
binomial distribution, we need ______ and______ to be
at least 5.

80. 80. True or False: The sample mean is an unbiased T

estimate of the population mean.

81. 81. True or False: The sample proportion is an unbi- T

ased estimate of the population proportion.

82. 82. True or False: The mean of the sampling distribu- T

tion of a sample proportion is the population propor-
tion,π .

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83. 83. True or False: The standard error of the sampling F

distribution of a sample proportion is căn p(1-p)/n
where p is the sample proportion.

84. 84. True or False: The standard deviation of the sam- T

pling distribution of a sample proportion is căn π(1-π
)/n where π is the population proportion.

85. 85. True or False: A sample of size 25 provides a sam- T

ple variance of 400. The standard error, in this case
equal to 4, is best described as the estimate of the
standard deviation of means calculated from samples
of size 25.

86. 86. True or False: An unbiased estimator will have a T

value, on average across samples, equal to the popu-
lation parameter value.

87. 87. True or False: In inferential statistics, the standard T

error of the sample mean assesses the uncertainty or
error of estimation.

88. 88. True or False: The sample proportion is an unbi- T

ased estimator for the population proportion.

89. 89. True or False: The sample mean is an unbiased T

estimator for the population mean.

90. 90. Assume that house prices in a neighborhood 0.3173 using Excel or
are normally distributed with a standard deviation of 0.3174 using Table E.2
$20,000. A random sample of 16 observations is taken.
What is the probability that the sample mean differs
from the population mean by more than $5,000?

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91. SCENARIO 7-1 0.3085

The time spent studying by students in the week be-
fore final exams follows a normal distribution with a
standard deviation of 8 hours. A random sample of
4 students was taken in order to estimate the mean
study time for the population of all students.

91. Referring to Scenario 7-1, what is the probability

that the sample mean exceeds the population mean
by more than 2 hours?

92. 92. Referring to Scenario 7-1, what is the probability 0.2266

that the sample mean is more than 3 hours below the
population mean?

93. 93. Referring to Scenario 7-1, what is the probability 0.3829 using Excel or
that the sample mean differs from the population 0.3830 using Table E.2
mean by less than 2 hours?

94. 94. Referring to Scenario 7-1, what is the probability 0.4533 using Excel or
that the sample mean differs from the population 0.4532 using Table E.2
mean by more than 3 hours?

95. SCENARIO 7-2 0.9772

The mean selling price of new homes in a small town
over a year was $115,000. The population standard
deviation was $25,000. A random sample of 100 new
home sales from this city was taken.

95. Referring to Scenario 7-2, what is the probability

that the sample mean selling price was more than
$110,000?

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96. 96. Referring to Scenario 7-2, what is the probabili- 0.5763 using Excel or
ty that the sample mean selling price was between 0.5762 using Table E.2
$113,000 and $117,000?

97. 97. Referring to Scenario 7-2, what is the probabili- 0.3108

ty that the sample mean selling price was between
$114,000 and $116,000?

98. 98. Referring to Scenario 7-2, without doing the cal- b

culations, state in which of the following ranges the
sample mean selling price is most likely to lie?
a) $113,000 -- $115,000
b) $114,000 -- $116,000
c) $115,000 -- $117,000
d) $116,000 -- $118,000

99. SCENARIO 7-3 0.8413

The lifetimes of a certain brand of light bulbs are
known to be normally distributed with a mean of 1,600
hours and a standard deviation of 400 hours. A ran-
dom sample of 64 of these light bulbs is taken.

99. Referring to Scenario 7-3, what is the probability

that the sample mean lifetime is more than 1,550
hours?

100. 100. Referring to Scenario 7-3, the probability is 0.15 1,651.82 hours using Ex-
that the sample mean lifetime is more than how many cel or 1,652 hours using
hours? Table E.2

101. 101. Referring to Scenario 7-3, the probability is 0.20 64.08 hours using Excel or
that the sample mean lifetime differs from the popu- 64 hours using Table E.2
lation mean lifetime by at least how many hours?
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102. SCENARIO 7-4 0.15 or 15%

According to a survey, only 15% of customers who
visited the web site of a major retail store made a
purchase. Random samples of size 50 are selected.

102. Referring to Scenario 7-4, the mean of all the

sample proportions of customers who will make a
purchase after visiting the web site is _______.

103. 103. Referring to Scenario 7-4, the standard deviation 0.05050

of all the sample proportions of customers who will
make a purchase after visiting the web site is ________.

104. 104. True or False: Referring to Scenario 7-4, the re- T

quirements for using a normal distribution to approx-
imate a binomial distribution is fulfilled.

105. 105. Referring to Scenario 7-4, what proportion of the 0.1596

samples will have between 20% and 30% of customers
who will make a purchase after visiting the web site?

106. 106. Referring to Scenario 7-4, what proportion of the 0.5

samples will have less than 15% of customers who will
make a purchase after visiting the web site?

107. 107. Referring to Scenario 7-4, what is the probability 0.0015

that a random sample of 50 will have at least 30% of
customers who will make a purchase after visiting the
web site?

108. 108. Referring to Scenario 7-4, 90% of the samples will 21.47%
have less than what percentage of customers who will
make a purchase after visiting the web site?
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109. 109. Referring to Scenario 7-4, 90% of the samples will 8.528% using Excel or
have more than what percentage of customers who 8.536% using Table E.2
will make a purchase after visiting the web site?

110. 110. A study at a college in the west coast reveals that, 45%
historically, 45% of the students are minority students.
The expected percentage of minority students in their
next group of freshmen is _______.

111. 111. A study at a college in the west coast reveals 0.05745

that, historically, 45% of the students are minority
students. If random samples of size 75 are selected,
the standard error of the proportion of students in the
samples who are minority students is _________.

112. 112. A study at a college in the west coast reveals that, 0.8034 using Excel or
historically, 45% of the students are minority students. 0.8033 using Table E.2
If a random sample of size 75 is selected, the probabili-
ty is _______ that between 30% and 50% of the students
in the sample will be minority students.

113. 113. A study at a college in the west coast reveals that, 0.1920 using Excel or
historically, 45% of the students are minority students. 0.1922 using Table E.2
If a random sample of size 75 is selected, the proba-
bility is _______ that more than half of the students in
the sample will be minority students.

114. 114. A study at a college in the west coast reveals that, 49.83
historically, 45% of the students are minority students.
If random samples of size 75 are selected, 80% of
the samples will have less than ______% of minority
students.

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115. 115. A study at a college in the west coast reveals that, 35.55
historically, 45% of the students are minority students.
If random samples of size 75 are selected, 95% of
the samples will have more than ______% of minority
students.

116. 116. Referring to Scenario 7-5, the population mean of 19% or 0.19
all the sample proportions is ______.

117. 117. Referring to Scenario 7-5, the standard error of 0.0277

all the sample proportions is ______.

118. 118. Referring to Scenario 7-5, among all the random 92.85 using Excel or 92.82
samples of size 200, ______ % will have between 14% using Table E.2
and 24% who have high-speed access to the Internet.

119. 119. Referring to Scenario 7-5, among all the random 99.97
samples of size 200, ______ % will have between 9% and
29% who have high-speed access to the Internet.

120. 120. Referring to Scenario 7-5, among all the random 0.0000 or virtually zero
samples of size 200, ______ % will have more than 30%
who have high-speed access to the Internet.

121. 121. Referring to Scenario 7-5, among all the random 64.08 using Excel or 64.06
samples of size 200, ______ % will have less than 20% using Table E.2
who have high-speed access to the Internet.

122. 122. Referring to Scenario 7-5, among all the random 22.56 using Excel or 22.55
samples of size 200, 90 % will have less than _____% using Table E.2
who have high-speed access to the Internet.

123. 15.45

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123. Referring to Scenario 7-5, among all the random

samples of size 200, 90 % will have more than _____%
who have high-speed access to the Internet.

124. SCENARIO 7-6 0.375 or 37.5%

Online customer service is a key element to success-
ful online retailing. According to a marketing survey,
37.5% of online customers take advantage of the on-
line customer service. Random samples of 200 cus-
tomers are selected.

124. Referring to Scenario 7-6, the population mean of

all possible sample proportions is ______.

125. 125. Referring to Scenario 7-6, the standard error of 0.0342

all possible sample proportions is ______.

126. 126. Referring to Scenario 7-6, ____ % of the samples 53.48 using Excel or 53.46
are likely to have between 35% and 40% who take using Table E.2
advantage of online customer service.

127. 127. Referring to Scenario 7-6, ____ % of the samples 50

are likely to have less than 37.5% who take advantage
of online customer service.

128. 128. Referring to Scenario 7-6, 90% of the sam- 31.87 and 43.13
ples proportions symmetrically around the popula-
tion proportion will have between _____% and _____%
of the customers who take advantage of online cus-
tomer service.

129. 129. Referring to Scenario 7-6, 95% of the sam- 30.79 and 44.21
ples proportions symmetrically around the popula-

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tion proportion will have between _____% and _____%

of the customers who take advantage of online cus-
tomer service.

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