Business Statistics In Practice, 3rd Canadian Edition By Bruce - Test Bank

Business Statistics In Practice, 3rd Canadian Edition By Bruce – Test Bank

 

Instant Download – Complete Test Bank With Answers

 

 

Sample Questions Are Posted Below

 

c6

Student: ___________________________________________________________________________

1. If we have a sample size of 100 and a population proportion of 0.10, we can approximate the sampling distribution of  with a normal distribution.
   True    False

 

2. If we have a sample size of 500 and a population proportion of 0.995, we can approximate the sampling distribution of  with a normal distribution.
   True    False

 

3. The sampling distribution of  must be a normal distribution with a mean 0 and standard deviation 1.
   True    False

 

4. For any sampled population and any sample size, the population of all sample means is approximately normally distributed.
   True    False

 

5. The sampling distribution of the sample mean  is the probability distribution of the population of all possible values of the sample mean that could be obtained from all possible samples of the same sample size.
   True    False

 

6. A sample statistic is an unbiased point estimate of a population parameter if the mean of the populations of all possible values of the sample statistic equals the population parameter.
   True    False

 

7. A minimum variance unbiased point estimate has a variance that is as small as or smaller than the variances of any other unbiased point estimate.
   True    False

 

8. The sample mean is always equal to the population mean whenever the sample mean is computed from 30 or more observations.
   True    False

 

9. The reason sample variance has a divisor of n-1 rather than n is that it makes the variance an unbiased estimate of the population variance.
   True    False

 

10. The standard deviation of all possible sample proportions increases as the sample size increases.
    True    False

 

11. Like the Empirical Rule, the Central Limit Theorem is only applicable to symmetric distributions.
    True    False

 

12. If a population is known to be normally distributed, then it follows that the sample standard deviation s must equal the population standard deviation .
    True    False

 

13. If the sampled population has a normal distribution, then the sampling distribution of  is also normal regardless of the sample size.
    True    False

 

14. If a population is known to be normally distributed, then it follows that the sample mean  must equal the population mean   .
    True    False

 

15. If p = .8 and n = 50, then we can conclude that the sampling distribution of  is approximately a normal distribution.
    True    False

 

16. If p = .9 and n = 40, then we can conclude that the sampling distribution of  is approximately a normal distribution.
    True    False

 

17. If the sampled population distribution is skewed, then in most cases the sampling distribution of the sample mean  can be approximated by the normal distribution if the sample size n is at least 30.
    True    False

 

18. The sampling distribution of a sample proportion is approximately normal if and only if np  5.
    True    False

 

19. As the sample size increases, the mean of the sampling distribution of  decreases.
    True    False

 

20. If we take a sample of any size from a population with mean  and standard deviation   , then the standard deviation of the sampling distribution of the sample mean   is   .
    True    False

 

21. The mean of the sampling distribution of  is always equal to the mean   of the sampled population.
    True    False

 

22. For a finite population, the sampling distribution of the sample mean  can be developed by repeatedly taking all samples of size n and computing the sample means and reporting the resulting sample means in the form of a probability distribution.
    True    False

 

23. The sample variance s² is an unbiased estimator of the population variance  .
    True    False

 

24. The sample standard deviation s is an unbiased estimator of the population standard deviation  .
    True    False

 

25. The central limit theorem states that if the sample size is sufficiently large, then the sampling distribution of the sample ________ is approximately normal, even if the sampled population is not normally distributed.
    A. median
    B. mode
    C. standard deviation
    D. variance
    E. mean

 

26. Suppose you take a sample of size 4 from a population with a mean of 70 and a standard deviation of 10. Based on such a sample, what are the mean and standard deviation of the sampling distribution of  ?
    A. = 70, = 5
    B. = 70, = 2.5
    C. = 17.5, = 5
    D. = 17.5, = 10
    E. Cannot be determined unless the sample size is at least 30.

 

27. As the sample size ______________ the variance of the sampling distribution of  ___________.
    A. decreases, decreases
    B. increases, remains the same
    C. decreases, remains the same
    D. increases, decreases
    E. increases, increases

 

28. Consider a sampling distribution formed based on n = 9. If the standard deviation of the population of individual measurements is  , then the standard deviation of the population of all sample means   equals ____.
    A.
    B.
    C.
    D.
    E.

 

29. If the sampled population has a mean of 48 and standard deviation of 16, then for a sample of size n = 16 the sampling distribution of   has a mean of ____ and a standard deviation of ____.
    A. 4 and 1
    B. 12 and 4
    C. 48 and 4
    D. 48 and 1
    E. 48 and 16

 

A manufacturing company measures the weight of boxes before shipping them to the customers. If the box weights have a population mean and standard deviation of 90 kg and 24 kg respectively, then based on a sample size of 36 boxes, the probability that the average weight of the boxes will:

 

30. Exceed 94 kg is:
    A. 0.3413
    B. 0.8413
    C. 0.1587
    D. 0.5636
    E. 0.1687

 

31. Be less than 84 kg is:
    A. 0.1687
    B. 0.9332
    C. 0.4332
    D. 0.0668
    E. 0.8413

 

32. The population of all sample proportions has an approximately normal distribution if the sample size (n) is sufficiently large. The rule of thumb for ensuring that n is sufficiently large is:
    A. np ³ 5
    B. n(1 – p) ³ 5
    C. np £ 5
    D. n(1 – p) £ 5 and np £ 5
    E. np ³ 5 and n(1 – p) ³ 5

 

33. If we have a sample size of 100 and a population proportion of 0.10, the standard deviation of the sampling distribution of  is ____.
    A. 10
    B. 9
    C. 0.03
    D. 3
    E. 90

 

34. Whenever the sampled population has a normal distribution, the sampling distribution of  is normal:
    A. for only large sample sizes.
    B. for only small sample sizes.
    C. for any sample size.
    D. for only samples of exactly 30.
    E. for only samples of sizes greater than 31.

 

35. If a population distribution is known to be normal, then it follows that:
    A. the sample mean must equal the population mean.
    B. the sample mean must equal the population mean for large samples.
    C. the sample standard deviation must equal the population standard deviation.
    D. the sample distribution of the sample mean is approximately normal.
    E. the sample distribution of the sample mean is exactly normal.

 

36. If we have a sample size of 100 and a population proportion of 0.10, the mean of the sampling distribution of  is ____.
    A. 1000
    B. 10
    C. 1
    D. 0.10
    E. 0.01

 

37. The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are delinquent more than 90 days overdue. The historical records of the company show that over the past 8 years 13 percent of the accounts are delinquent. For this quarter, the auditing staff randomly selected 250 customer accounts. What is the probability that no more than 40 accounts will be classified as delinquent?
    A. 0.4207
    B. 0.9207
    C. 0.0793
    D. 0.4015
    E. 0.9015

 

The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are delinquent more than 90 days overdue. The historical records of the company show that over the past 8 years, 14 percent of the accounts are delinquent. For this quarter, the auditing staff randomly selected 250 customer accounts.

 

38. What is the probability that at least 30 accounts will be classified as delinquent?
    A. 0.3186
    B. 0.1814
    C. 0.8186
    D. 0.6372
    E. 0.7584

 

39. What are the mean and the standard deviation of the sampling distribution of  ?
    A. 14 and 250
    B. 14 and .1204
    C. 35 and 5.486
    D. 14 and .0219
    E. 35 and 30.1

 

According to a hospital administrator, historical records over the past 10 years have shown that 20% of the major surgery patients are dissatisfied with after-surgery care in the hospital. A scientific poll based on 400 hospital patients has just been conducted.

 

40. What is the probability that less than 64 patients will not be satisfied with the after-surgery care?
    A. 0.4772
    B. 0.0228
    C. 0.9772
    D. 0.9544
    E. 0.0197

 

41. What is the probability that at least 70 patients will not be satisfied with the after-surgery care?
    A. 0.8944
    B. 0.3944
    C. 0.1056
    D. 0.7888
    E. 0.8449

 

42. What are the mean and the standard deviation of the sampling distribution of  ?
    A. 0.16 and 0.0004
    B. 0.16 and 0.02
    C. 0.20 and 0.02
    D. 0.20 and 0.0004
    E. 0.20 and 0.16

 

43. For non-normal populations, as the sample size ___________________, the distribution of sample means approaches a ________________ distribution.
    A. decreases; uniform
    B. increases; normal
    C. decreases; normal
    D. increases; uniform
    E. increases; exponential

 

In a manufacturing process a machine produces bolts. The lengths of the bolts follow a normal distribution with an average of 3 cm and a variance of 0.03 cm². If we randomly select three bolts from this process:

 

44. What is the standard deviation of the sample mean?
    A. 03
    B. 01
    C. 1732
    D. 0577
    E. 10

 

45. What is the probability the mean length of the bolt is at least 3.16 cm?
    A. 0.9772
    B. 0.0548
    C. 0.9452
    D. 0.4452
    E. 0.0228

 

46. What is the probability the mean length of the bolt is at most 3.1 cm?
    A. 0.8413
    B. 1
    C. 0.7157
    D. 0.2843
    E. 0.1587

 

47. Suppose you take a random sample from a normally distributed population with mean  = 175 and compute the sample mean   . If   = 9, find P(   > 172).
    A. 0300
    B. 0100
    C. 1732
    D. 0577
    E. 8413

 

48. Suppose you take a random sample from a normally distributed population with mean  = 16 and compute the sample mean   . If   = 4, find P(   < 25).
    A. 0300
    B. 1.000
    C. 1732
    D. 0577
    E. 8413

 

49. Suppose you take a random sample from a normally distributed population with mean  = 2500 and compute the sample mean   . If   = 7, find P(   > 2510).
    A. 0000
    B. 9878
    C. 1732
    D. 0577
    E. 8413

 

50. If  = 400, P(   < 396) =.0228, and n = 100, then the population standard deviation   is _____.
    A. 76
    B. 98
    C. 17
    D. 20
    E. 41

 

51. If we take a sample of size n = 100 from a population with  = 400 and   = 200, find P(   < 402).
    A. 0764
    B. 9878
    C. 1732
    D. 5398
    E. 8413

 

52. If we take a sample of size n = 100 from a population with  = 400 and   = 20, find P(395.4 <   < 404.6).
    A. 9786
    B. 9878
    C. 1732
    D. 5398
    E. 8413

 

53. The number of defectives in the samples of 50 observations each are the following: 5,1,1,2,3,3,1,4,2,3. What is the estimate of the population proportion of defectives?
    A. 0399
    B. 0098
    C. 1700
    D. 0500
    E. 0813

 

54. The number of defectives in the samples of 100 observations each are the following: 1,2,1,0,2,3,1,4,2,1. What is the estimate of the population proportion of defectives?
    A. 0399
    B. 0098
    C. 0170
    D. 0500
    E. 0813

 

55. Suppose that 60 percent of the employees in a particular union support a candidate for union president. The probability that a sample of 1,000 employees would yield a sample proportion in favour of the candidate within 4 percentage points of the actual proportion is _____.
    A. 9786
    B. 9878
    C. 9902
    D. 5398
    E. 8413

 

56. Suppose that 60 percent of the employees in a particular union support a candidate for union president. The probability that a sample of 1,000 employees would yield a sample proportion in favour of the candidate within 2 percentage points is _____.
    A. 9786
    B. 9878
    C. 9902
    D. 8030
    E. 8413

 

57. The spread of the sampling distribution of  is ____________ than the spread of the corresponding population distribution.
    ________________________________________

 

58. Suppose you take a sample of 40 observations from a uniform distribution. Based on this sample, the sampling distribution of  is _______.
    ________________________________________

 

59. The _____ says that if the sample size is sufficiently large, then the sample means are approximately normally distributed even if the sampled population is not normal.
    ________________________________________

 

60. If a sample size is at least _____, then for any sampled population, we can conclude that the sample means are approximately normal.
    ________________________________________

 

61. The sample mean is an unbiased, _______-variance point estimate of the population mean.
    ________________________________________

 

62. If the sampled population is finite and at least _____ times larger than the sample size, then the finite population multiplier is approximately equal to one.
    ________________________________________

 

63. The notation for the standard deviation of the sample mean is also known as the standard __________.
    ________________________________________

 

64. The sampling distribution of the sample mean is approximately normal for sufficiently ________ sample sizes regardless of the distribution shape of the sampled population.
    ________________________________________

 

65. The _________ theorem allows us to approximate the sampling distribution of a sample mean with a normal probability distribution whenever the sample size is sufficiently large.
    ________________________________________

 

66. As the sample size increases the variability of the sampling distribution of the sample mean ______________.
    ________________________________________

 

67. As the sample size ___________, the variability of the sampling distribution of the sample proportion increases.
    ________________________________________

 

68. The population of all ___________ proportions is described by sampling distribution of  .
    ________________________________________

 

69. The _______________________ of the sample mean  is the probability distribution of the population of all possible sample means that could be obtained from all possible samples of the same size.
    ________________________________________

 

70. The ___________ is a minimum-variance unbiased point estimate of the population mean.
    ________________________________________

 

71. Suppose you take a random sample of size n = 16 from a normally distributed population with  = 40 and   = 16. Find P(  < 35).

 

 

 

 

72. A golf tournament organizer is attempting to determine whether hole (pin) placement has a significant impact on the average number of strokes for the 13^thhole on a given golf course. Historically, the pin has been placed in the front right corner of the green, and the historical mean number of strokes for the hole has been 4.25, with a standard deviation of 1.6 strokes. On a particular day during the most recent golf tournament, the organizer placed the hole (pin) in the back left corner of the green. 64 golfers played the hole with the new placement on that day. Determine the probability of the sample average number of strokes exceeding 4.75.

 

 

 

 

73. Packages of sugar bags for Sweeter Sugar Inc. have an average weight of 16 grams and a standard deviation of 0.2 grams. The weights of the sugar bags are normally distributed. What is the probability that 16 randomly selected packages will have a weight in excess of 16.075 grams?

 

 

 

 

74. The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 cm and a standard deviation of 0.3 cm. What is the probability that average length of a steel sheet from a sample of 9 units is more than 29.95 cm long?

 

 

 

 

75. Suppose you take a random sample from a normally distributed population with mean  = 175 and compute the sample mean   . If   = 9, find P(   < 170).

 

 

 

 

76. Suppose you take a random sample of size n = 4 from a normally distributed population with  = 16 and   = 8. Find P(  < 25).

 

 

 

 

77. Suppose you take a random sample from a normally distributed population with mean  = 2500 and compute the sample mean   . If   = 49, find P(  < 2488).

 

 

 

 

78. Suppose you take a random sample of size n = 100 from a population with  = 400. If P(  < 380) = 0.0668, find   .

 

 

 

 

79. Suppose you take a random sample of size n = 100 from a population with  = 400 and   = 200. Find P(  < 380).

 

 

 

 

80. Suppose you take a random sample of size n = 100 from a population with  = 400 and   = 20. Find P(396 <  < 401).

 

 

 

 

81. The number of defectives in the samples of 50 observations each are the following: 5,1,1,2,3,3,1,4,2,3. What is the estimate of the population proportion of defectives?

 

 

 

 

82. The number of defectives in the samples of 100 observations each are the following: 1,2,1,0,2,3,1,4,2,1. What is the estimate of the population proportion of defectives?

 

 

 

 

Suppose that 60 percent of the student voters in a particular university support a candidate for students’ council president. Find the probability that a sample of 1,000 student voters would yield a sample proportion in favour of the candidate within:

 

83. 4 percentage points of the actual proportion.

 

 

 

 

84. 2 percentage points.

 

 

 

 

85. Suppose you take a random sample of size n = 81 from a population with  = 1000 and   = 90. Find P(  > 1015).

 

 

 

 

A random sample of size 30 is taken from a population with mean 50 and standard deviation 5.

 

86. Describe the shape of the sampling distribution of  .

 

 

 

 

87. What is ?

 

 

 

 

88. What is ?

 

 

 

 

89. Find P ( > 49).

 

 

 

 

90. Find P ( < 48).

 

 

 

 

91. Find P ( > 50.5).

 

 

 

 

92. Find P ( < 51.5).

 

 

 

 

A random sample of size 1,000 is taken from a population where, for some characteristic of the population, p = .20.

 

93. Describe the shape of the sampling distribution of  .

 

 

 

 

94. What is ?

 

 

 

 

95. What is  ?

 

 

 

 

96. Find P( < .18).

 

 

 

 

97. Find P( > .175).

 

 

 

 

98. Find P( > .21).

 

 

 

 

99. Find P( < .22).

 

 

 

 

100. Packages of sugar bags for Sweeter Sugar Inc. have an average weight of 16 grams and a standard deviation of 0.3 grams. The weights of the sugar bags are normally distributed. What is the probability that 9 randomly selected packages will have a weight in excess of 16.025 grams?

 

 

 

 

The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 cm and a standard deviation of 0.2 cm.

 

101. What is the probability that randomly selected 4 sheets will have an average length of less than 29.9 cm long?

 

 

 

 

102. A sample of four metal sheets is randomly selected from a batch. What is the probability that the average length of a sheet is between 30.25 and 30.35 cm long?

 

 

 

 

103. Suppose the standard deviation increases to 0.3 cm. What is the probability that average length of a steel sheet from a sample of 9 units is more than 29.95 cm long?

 

 

 

 

The chief chemist for a major oil/gasoline production company claims that the regular unleaded gasoline produced by the company contains on average 4 grams of a certain ingredient. The chemist further states that the distribution of this ingredient per L of regular unleaded gasoline is normal and has a standard deviation of 1.2 grams.

 

104. What is the probability of finding an average in excess of 4.3 grams of this ingredient from randomly inspected 100L of regular unleaded gasoline?

 

 

 

 

105. What is the probability of finding an average less than 3.85 grams of this ingredient from randomly inspected 64L of regular unleaded gasoline?

 

 

 

 

In the upcoming students’ council election, the most recent poll based on 900 students predicts that the incumbent will be re-elected with 55% of the votes.

 

106. From the 900 students, how many indicated that they would not vote for the current students’ council president or indicated that they were undecided?

 

 

 

 

107. What is ?

 

 

 

 

108. For the sake of argument, assume that 51% of the actual student voters in the university support the incumbent council president (p = 0.51). Calculate the probability of observing a sample proportion of voters 0.55 or higher supporting the incumbent council president.

 

 

 

 

It has been reported that the average time to download the home page from a government website was 0.9 seconds. Suppose that the download times were normally distributed with a standard deviation of 0.3 seconds. If random samples of 36 download times are selected:

 

109. Describe the shape of the sampling distribution. How was this determined?

 

 

 

 

110. Calculated the mean of the sampling distribution of the sampling mean.

 

 

 

 

111. Calculate the standard deviation of the sampling distribution of the sample mean.

 

 

 

 

112. 80% of the sample means will be between what two values symmetrically distributed around the population mean.

 

 

 

 

113. What is the probability that the sample mean will be less than 0.80 seconds?

 

 

 

 

A standardized test has a   =3.5 and   =0.5. Suppose a random sample of 100 individual test scores is selected.

 

114. What is  ?

 

 

 

 

115. Calculated  .

 

 

 

 

116. Find the interval that contains 95.44% of the sample means.

 

 

 

 

117. What is the probability that the random sample of 100 test scores have a mean greater than 3.65?

 

 

 

 

The diameter of small toy balls manufactured at a factory is expected to be approximately normally distributed with a mean of 5.2 cm and a standard deviation of .08 cm. Suppose a random sample of 20 balls are selected.

 

118. Calculate the mean of the sampling distribution of the sample mean.

 

 

 

 

119. Calculate the standard deviation of the sampling distribution of the sample mean.

 

 

 

 

120. Find the interval that contains 95.44% of the sample means.

 

 

 

 

121. What percentage of sample means will be less than 5.00 cm?

 

 

 

 

122. The mean of the sampling distribution of the sample proportion  is equal to _____.

 

 

 

 

 

 

c6 Key

1. If we have a sample size of 100 and a population proportion of 0.10, we can approximate the sampling distribution of  with a normal distribution.
   TRUE

 

Bowerman – Chapter 06 #1
Difficulty: Easy
Learning Objective: 06-03 Use the sampling distribution of the sample proportion
 

2. If we have a sample size of 500 and a population proportion of 0.995, we can approximate the sampling distribution of  with a normal distribution.
   FALSE

 

Bowerman – Chapter 06 #2
Difficulty: Medium
Learning Objective: 06-03 Use the sampling distribution of the sample proportion
 

3. The sampling distribution of  must be a normal distribution with a mean 0 and standard deviation 1.
   FALSE

 

Bowerman – Chapter 06 #3
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

4. For any sampled population and any sample size, the population of all sample means is approximately normally distributed.
   FALSE

 

Accessibility: Keyboard Navigation
Bowerman – Chapter 06 #4
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

5. The sampling distribution of the sample mean  is the probability distribution of the population of all possible values of the sample mean that could be obtained from all possible samples of the same sample size.
   TRUE

 

Bowerman – Chapter 06 #5
Difficulty: Easy
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

6. A sample statistic is an unbiased point estimate of a population parameter if the mean of the populations of all possible values of the sample statistic equals the population parameter.
   TRUE

 

Accessibility: Keyboard Navigation
Bowerman – Chapter 06 #6
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

7. A minimum variance unbiased point estimate has a variance that is as small as or smaller than the variances of any other unbiased point estimate.
   TRUE

 

Accessibility: Keyboard Navigation
Bowerman – Chapter 06 #7
Difficulty: Medium
Learning Objective: N/A
 

8. The sample mean is always equal to the population mean whenever the sample mean is computed from 30 or more observations.
   FALSE

 

Accessibility: Keyboard Navigation
Bowerman – Chapter 06 #8
Difficulty: Medium
Learning Objective: 06-02 Explain the central limit theorem
 

9. The reason sample variance has a divisor of n-1 rather than n is that it makes the variance an unbiased estimate of the population variance.
   TRUE

 

Accessibility: Keyboard Navigation
Bowerman – Chapter 06 #9
Difficulty: Hard
Learning Objective: N/A
 

10. The standard deviation of all possible sample proportions increases as the sample size increases.
    FALSE

 

Accessibility: Keyboard Navigation
Bowerman – Chapter 06 #10
Difficulty: Medium
Learning Objective: 06-03 Use the sampling distribution of the sample proportion
 

11. Like the Empirical Rule, the Central Limit Theorem is only applicable to symmetric distributions.
    FALSE

 

Accessibility: Keyboard Navigation
Bowerman – Chapter 06 #11
Difficulty: Medium
Learning Objective: N/A
 

12. If a population is known to be normally distributed, then it follows that the sample standard deviation s must equal the population standard deviation .
    FALSE

 

Bowerman – Chapter 06 #12
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

13. If the sampled population has a normal distribution, then the sampling distribution of  is also normal regardless of the sample size.
    TRUE

 

Bowerman – Chapter 06 #13
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

14. If a population is known to be normally distributed, then it follows that the sample mean  must equal the population mean   .
    FALSE

 

Bowerman – Chapter 06 #14
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

15. If p = .8 and n = 50, then we can conclude that the sampling distribution of  is approximately a normal distribution.
    TRUE

 

Bowerman – Chapter 06 #15
Difficulty: Easy
Learning Objective: 06-03 Use the sampling distribution of the sample proportion
 

16. If p = .9 and n = 40, then we can conclude that the sampling distribution of  is approximately a normal distribution.
    FALSE

 

Bowerman – Chapter 06 #16
Difficulty: Medium
Learning Objective: 06-03 Use the sampling distribution of the sample proportion
 

17. If the sampled population distribution is skewed, then in most cases the sampling distribution of the sample mean  can be approximated by the normal distribution if the sample size n is at least 30.
    TRUE

 

Bowerman – Chapter 06 #17
Difficulty: Easy
Learning Objective: 06-02 Explain the central limit theorem
 

18. The sampling distribution of a sample proportion is approximately normal if and only if np  5.
    FALSE

 

Bowerman – Chapter 06 #18
Difficulty: Medium
Learning Objective: 06-03 Use the sampling distribution of the sample proportion
 

19. As the sample size increases, the mean of the sampling distribution of  decreases.
    FALSE

 

Bowerman – Chapter 06 #19
Difficulty: Easy
Learning Objective: N/A
 

20. If we take a sample of any size from a population with mean  and standard deviation   , then the standard deviation of the sampling distribution of the sample mean   is   .
    FALSE

 

Bowerman – Chapter 06 #20
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

21. The mean of the sampling distribution of  is always equal to the mean   of the sampled population.
    TRUE

 

Bowerman – Chapter 06 #21
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

22. For a finite population, the sampling distribution of the sample mean  can be developed by repeatedly taking all samples of size n and computing the sample means and reporting the resulting sample means in the form of a probability distribution.
    TRUE

 

Bowerman – Chapter 06 #22
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

23. The sample variance s² is an unbiased estimator of the population variance  .
    TRUE

 

Bowerman – Chapter 06 #23
Difficulty: Medium
Learning Objective: N/A
 

24. The sample standard deviation s is an unbiased estimator of the population standard deviation  .
    FALSE

 

Bowerman – Chapter 06 #24
Difficulty: Medium
Learning Objective: N/A
 

25. The central limit theorem states that if the sample size is sufficiently large, then the sampling distribution of the sample ________ is approximately normal, even if the sampled population is not normally distributed.
    A.median
    B. mode
    C. standard deviation
    D. variance
    E. mean

 

Accessibility: Keyboard Navigation
Bowerman – Chapter 06 #25
Difficulty: Medium
Learning Objective: 06-02 Explain the central limit theorem
 

26. Suppose you take a sample of size 4 from a population with a mean of 70 and a standard deviation of 10. Based on such a sample, what are the mean and standard deviation of the sampling distribution of  ?
    A. = 70, = 5
    B. = 70, = 2.5
    C. = 17.5, = 5
    D. = 17.5, = 10
    E. Cannot be determined unless the sample size is at least 30.

 

Bowerman – Chapter 06 #26
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

27. As the sample size ______________ the variance of the sampling distribution of  ___________.
    A. decreases, decreases
    B. increases, remains the same
    C. decreases, remains the same
    D. increases, decreases
    E. increases, increases

 

Accessibility: Keyboard Navigation
Bowerman – Chapter 06 #27
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

28. Consider a sampling distribution formed based on n = 9. If the standard deviation of the population of individual measurements is  , then the standard deviation of the population of all sample means   equals ____.
    A.
    B.
    C.
    D.
    E.

 

Bowerman – Chapter 06 #28
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

29. If the sampled population has a mean of 48 and standard deviation of 16, then for a sample of size n = 16 the sampling distribution of   has a mean of ____ and a standard deviation of ____.
    A. 4 and 1
    B. 12 and 4
    C. 48 and 4
    D. 48 and 1
    E. 48 and 16

 

Bowerman – Chapter 06 #29
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

A manufacturing company measures the weight of boxes before shipping them to the customers. If the box weights have a population mean and standard deviation of 90 kg and 24 kg respectively, then based on a sample size of 36 boxes, the probability that the average weight of the boxes will:

 

Bowerman – Chapter 06
 

30. Exceed 94 kg is:
    A.0.3413
    B. 0.8413
    C. 0.1587
    D. 0.5636
    E. 0.1687

 

Accessibility: Keyboard Navigation
Bowerman – Chapter 06 #30
Difficulty: Medium
Learning Objective: N/A
 

31. Be less than 84 kg is:
    A.0.1687
    B. 0.9332
    C. 0.4332
    D. 0.0668
    E. 0.8413

 

Accessibility: Keyboard Navigation
Bowerman – Chapter 06 #31
Difficulty: Medium
Learning Objective: N/A
 

32. The population of all sample proportions has an approximately normal distribution if the sample size (n) is sufficiently large. The rule of thumb for ensuring that n is sufficiently large is:
    A.np ³ 5
    B. n(1 – p) ³ 5
    C. np £ 5
    D. n(1 – p) £ 5 and np £ 5
    E. np ³ 5 and n(1 – p) ³ 5

 

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Bowerman – Chapter 06 #32
Difficulty: Medium
Learning Objective: N/A
 

33. If we have a sample size of 100 and a population proportion of 0.10, the standard deviation of the sampling distribution of  is ____.
    A. 10
    B. 9
    C. 0.03
    D. 3
    E. 90

 

Bowerman – Chapter 06 #33
Difficulty: Medium
Learning Objective: 06-03 Use the sampling distribution of the sample proportion
 

34. Whenever the sampled population has a normal distribution, the sampling distribution of  is normal:
    A. for only large sample sizes.
    B. for only small sample sizes.
    C. for any sample size.
    D. for only samples of exactly 30.
    E. for only samples of sizes greater than 31.

 

Bowerman – Chapter 06 #34
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

35. If a population distribution is known to be normal, then it follows that:
    A.the sample mean must equal the population mean.
    B. the sample mean must equal the population mean for large samples.
    C. the sample standard deviation must equal the population standard deviation.
    D. the sample distribution of the sample mean is approximately normal.
    E. the sample distribution of the sample mean is exactly normal.

 

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Bowerman – Chapter 06 #35
Difficulty: Easy
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

36. If we have a sample size of 100 and a population proportion of 0.10, the mean of the sampling distribution of  is ____.
    A. 1000
    B. 10
    C. 1
    D. 0.10
    E. 0.01

 

Bowerman – Chapter 06 #36
Difficulty: Easy
Learning Objective: 06-03 Use the sampling distribution of the sample proportion
 

37. The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are delinquent more than 90 days overdue. The historical records of the company show that over the past 8 years 13 percent of the accounts are delinquent. For this quarter, the auditing staff randomly selected 250 customer accounts. What is the probability that no more than 40 accounts will be classified as delinquent?
    A.0.4207
    B. 0.9207
    C. 0.0793
    D. 0.4015
    E. 0.9015

 

Accessibility: Keyboard Navigation
Bowerman – Chapter 06 #37
Difficulty: Hard
Learning Objective: N/A
 

The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are delinquent more than 90 days overdue. The historical records of the company show that over the past 8 years, 14 percent of the accounts are delinquent. For this quarter, the auditing staff randomly selected 250 customer accounts.

 

Bowerman – Chapter 06
 

38. What is the probability that at least 30 accounts will be classified as delinquent?
    A.0.3186
    B. 0.1814
    C. 0.8186
    D. 0.6372
    E. 0.7584

 

Accessibility: Keyboard Navigation
Bowerman – Chapter 06 #38
Difficulty: Hard
Learning Objective: N/A
 

39. What are the mean and the standard deviation of the sampling distribution of  ?
    A. 14 and 250
    B. 14 and .1204
    C. 35 and 5.486
    D. 14 and .0219
    E. 35 and 30.1

 

Bowerman – Chapter 06 #39
Difficulty: Medium
Learning Objective: 06-03 Use the sampling distribution of the sample proportion
 

According to a hospital administrator, historical records over the past 10 years have shown that 20% of the major surgery patients are dissatisfied with after-surgery care in the hospital. A scientific poll based on 400 hospital patients has just been conducted.

 

Bowerman – Chapter 06
 

40. What is the probability that less than 64 patients will not be satisfied with the after-surgery care?
    A.0.4772
    B. 0.0228
    C. 0.9772
    D. 0.9544
    E. 0.0197

 

Accessibility: Keyboard Navigation
Bowerman – Chapter 06 #40
Difficulty: Hard
Learning Objective: N/A
 

41. What is the probability that at least 70 patients will not be satisfied with the after-surgery care?
    A.0.8944
    B. 0.3944
    C. 0.1056
    D. 0.7888
    E. 0.8449

 

Accessibility: Keyboard Navigation
Bowerman – Chapter 06 #41
Difficulty: Hard
Learning Objective: N/A
 

42. What are the mean and the standard deviation of the sampling distribution of  ?
    A. 0.16 and 0.0004
    B. 0.16 and 0.02
    C. 0.20 and 0.02
    D. 0.20 and 0.0004
    E. 0.20 and 0.16

 

Bowerman – Chapter 06 #42
Difficulty: Hard
Learning Objective: 06-03 Use the sampling distribution of the sample proportion
 

43. For non-normal populations, as the sample size ___________________, the distribution of sample means approaches a ________________ distribution.
    A.decreases; uniform
    B. increases; normal
    C. decreases; normal
    D. increases; uniform
    E. increases; exponential

 

Accessibility: Keyboard Navigation
Bowerman – Chapter 06 #43
Difficulty: Hard
Learning Objective: 06-02 Explain the central limit theorem
 

In a manufacturing process a machine produces bolts. The lengths of the bolts follow a normal distribution with an average of 3 cm and a variance of 0.03 cm². If we randomly select three bolts from this process:

 

Bowerman – Chapter 06
 

44. What is the standard deviation of the sample mean?
    A.03
    B. 01
    C. 1732
    D. 0577
    E. 10

 

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Bowerman – Chapter 06 #44
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

45. What is the probability the mean length of the bolt is at least 3.16 cm?
    A.0.9772
    B. 0.0548
    C. 0.9452
    D. 0.4452
    E. 0.0228

 

Accessibility: Keyboard Navigation
Bowerman – Chapter 06 #45
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

46. What is the probability the mean length of the bolt is at most 3.1 cm?
    A.0.8413
    B. 1
    C. 0.7157
    D. 0.2843
    E. 0.1587

 

Accessibility: Keyboard Navigation
Bowerman – Chapter 06 #46
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

47. Suppose you take a random sample from a normally distributed population with mean  = 175 and compute the sample mean   . If   = 9, find P(   > 172).
    A. 0300
    B. 0100
    C. 1732
    D. 0577
    E. 8413

 

Bowerman – Chapter 06 #47
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

48. Suppose you take a random sample from a normally distributed population with mean  = 16 and compute the sample mean   . If   = 4, find P(   < 25).
    A. 0300
    B. 1.000
    C. 1732
    D. 0577
    E. 8413

 

Bowerman – Chapter 06 #48
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

49. Suppose you take a random sample from a normally distributed population with mean  = 2500 and compute the sample mean   . If   = 7, find P(   > 2510).
    A. 0000
    B. 9878
    C. 1732
    D. 0577
    E. 8413

 

Bowerman – Chapter 06 #49
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

50. If  = 400, P(   < 396) =.0228, and n = 100, then the population standard deviation   is _____.
    A. 76
    B. 98
    C. 17
    D. 20
    E. 41

 

Bowerman – Chapter 06 #50
Difficulty: Hard
Learning Objective: N/A
 

51. If we take a sample of size n = 100 from a population with  = 400 and   = 200, find P(   < 402).
    A. 0764
    B. 9878
    C. 1732
    D. 5398
    E. 8413

 

Bowerman – Chapter 06 #51
Difficulty: Medium
Learning Objective: N/A
 

52. If we take a sample of size n = 100 from a population with  = 400 and   = 20, find P(395.4 <   < 404.6).
    A. 9786
    B. 9878
    C. 1732
    D. 5398
    E. 8413

 

Bowerman – Chapter 06 #52
Difficulty: Medium
Learning Objective: N/A
 

53. The number of defectives in the samples of 50 observations each are the following: 5,1,1,2,3,3,1,4,2,3. What is the estimate of the population proportion of defectives?
    A.0399
    B. 0098
    C. 1700
    D. 0500
    E. 0813

 

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Bowerman – Chapter 06 #53
Difficulty: Medium
Learning Objective: 06-03 Use the sampling distribution of the sample proportion
 

54. The number of defectives in the samples of 100 observations each are the following: 1,2,1,0,2,3,1,4,2,1. What is the estimate of the population proportion of defectives?
    A.0399
    B. 0098
    C. 0170
    D. 0500
    E. 0813

 

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Bowerman – Chapter 06 #54
Difficulty: Medium
Learning Objective: 06-03 Use the sampling distribution of the sample proportion
 

55. Suppose that 60 percent of the employees in a particular union support a candidate for union president. The probability that a sample of 1,000 employees would yield a sample proportion in favour of the candidate within 4 percentage points of the actual proportion is _____.
    A.9786
    B. 9878
    C. 9902
    D. 5398
    E. 8413

 

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Bowerman – Chapter 06 #55
Difficulty: Hard
Learning Objective: N/A
 

56. Suppose that 60 percent of the employees in a particular union support a candidate for union president. The probability that a sample of 1,000 employees would yield a sample proportion in favour of the candidate within 2 percentage points is _____.
    A.9786
    B. 9878
    C. 9902
    D. 8030
    E. 8413

 

Accessibility: Keyboard Navigation
Bowerman – Chapter 06 #56
Difficulty: Hard
Learning Objective: N/A
 

57. The spread of the sampling distribution of  is ____________ than the spread of the corresponding population distribution.
    Smaller

 

Bowerman – Chapter 06 #57
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

58. Suppose you take a sample of 40 observations from a uniform distribution. Based on this sample, the sampling distribution of  is _______.
    approximately normal

 

Bowerman – Chapter 06 #58
Difficulty: Medium
Learning Objective: 06-02 Explain the central limit theorem
 

59. The _____ says that if the sample size is sufficiently large, then the sample means are approximately normally distributed even if the sampled population is not normal.
    Central Limit Theorem

 

Bowerman – Chapter 06 #59
Difficulty: Hard
Learning Objective: 06-02 Explain the central limit theorem
 

60. If a sample size is at least _____, then for any sampled population, we can conclude that the sample means are approximately normal.
    30

 

Bowerman – Chapter 06 #60
Difficulty: Medium
Learning Objective: 06-02 Explain the central limit theorem
 

61. The sample mean is an unbiased, _______-variance point estimate of the population mean.
    minimum

 

Bowerman – Chapter 06 #61
Difficulty: Hard
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

62. If the sampled population is finite and at least _____ times larger than the sample size, then the finite population multiplier is approximately equal to one.
    20

 

Bowerman – Chapter 06 #62
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

63. The notation for the standard deviation of the sample mean is also known as the standard __________.
    error

 

Bowerman – Chapter 06 #63
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

64. The sampling distribution of the sample mean is approximately normal for sufficiently ________ sample sizes regardless of the distribution shape of the sampled population.
    large

 

Bowerman – Chapter 06 #64
Difficulty: Medium
Learning Objective: 06-02 Explain the central limit theorem
 

65. The _________ theorem allows us to approximate the sampling distribution of a sample mean with a normal probability distribution whenever the sample size is sufficiently large.
    Central Limit

 

Bowerman – Chapter 06 #65
Difficulty: Medium
Learning Objective: 06-02 Explain the central limit theorem
 

66. As the sample size increases the variability of the sampling distribution of the sample mean ______________.
    decreases

 

Bowerman – Chapter 06 #66
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

67. As the sample size ___________, the variability of the sampling distribution of the sample proportion increases.
    decreases

 

Bowerman – Chapter 06 #67
Difficulty: Medium
Learning Objective: 06-03 Use the sampling distribution of the sample proportion
 

68. The population of all ___________ proportions is described by sampling distribution of  .
    sample

 

Bowerman – Chapter 06 #68
Difficulty: Medium
Learning Objective: 06-03 Use the sampling distribution of the sample proportion
 

69. The _______________________ of the sample mean  is the probability distribution of the population of all possible sample means that could be obtained from all possible samples of the same size.
    sampling distribution

 

Bowerman – Chapter 06 #69
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

70. The ___________ is a minimum-variance unbiased point estimate of the population mean.
    sample mean

 

Bowerman – Chapter 06 #70
Difficulty: Medium
 

71. Suppose you take a random sample of size n = 16 from a normally distributed population with  = 40 and   = 16. Find P(  < 35).

0.1056

 

Bowerman – Chapter 06 #71
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

72. A golf tournament organizer is attempting to determine whether hole (pin) placement has a significant impact on the average number of strokes for the 13^thhole on a given golf course. Historically, the pin has been placed in the front right corner of the green, and the historical mean number of strokes for the hole has been 4.25, with a standard deviation of 1.6 strokes. On a particular day during the most recent golf tournament, the organizer placed the hole (pin) in the back left corner of the green. 64 golfers played the hole with the new placement on that day. Determine the probability of the sample average number of strokes exceeding 4.75.

P(   ³ 4.75) = .5 – .4938 = .0062

 

Bowerman – Chapter 06 #72
Difficulty: Hard
Learning Objective: N/A
 

73. Packages of sugar bags for Sweeter Sugar Inc. have an average weight of 16 grams and a standard deviation of 0.2 grams. The weights of the sugar bags are normally distributed. What is the probability that 16 randomly selected packages will have a weight in excess of 16.075 grams?

0.0668

 

Bowerman – Chapter 06 #73
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

74. The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 cm and a standard deviation of 0.3 cm. What is the probability that average length of a steel sheet from a sample of 9 units is more than 29.95 cm long?

0.8413

 

Bowerman – Chapter 06 #74
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

75. Suppose you take a random sample from a normally distributed population with mean  = 175 and compute the sample mean   . If   = 9, find P(   < 170).

0.0475

 

Bowerman – Chapter 06 #75
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

76. Suppose you take a random sample of size n = 4 from a normally distributed population with  = 16 and   = 8. Find P(  < 25).

.9878

 

Bowerman – Chapter 06 #76
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

77. Suppose you take a random sample from a normally distributed population with mean  = 2500 and compute the sample mean   . If   = 49, find P(  < 2488).

0.0436

 

Bowerman – Chapter 06 #77
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

78. Suppose you take a random sample of size n = 100 from a population with  = 400. If P(  < 380) = 0.0668, find   .

133

 

Bowerman – Chapter 06 #78
Difficulty: Hard
Learning Objective: N/A
 

79. Suppose you take a random sample of size n = 100 from a population with  = 400 and   = 200. Find P(  < 380).

0.1587

 

Bowerman – Chapter 06 #79
Difficulty: Medium
Learning Objective: N/A
 

80. Suppose you take a random sample of size n = 100 from a population with  = 400 and   = 20. Find P(396 <  < 401).

0.6687

 

Bowerman – Chapter 06 #80
Difficulty: Medium
Learning Objective: N/A
 

81. The number of defectives in the samples of 50 observations each are the following: 5,1,1,2,3,3,1,4,2,3. What is the estimate of the population proportion of defectives?

.05

 

Bowerman – Chapter 06 #81
Difficulty: Medium
Learning Objective: 06-03 Use the sampling distribution of the sample proportion
 

82. The number of defectives in the samples of 100 observations each are the following: 1,2,1,0,2,3,1,4,2,1. What is the estimate of the population proportion of defectives?

.017

 

Bowerman – Chapter 06 #82
Difficulty: Medium
Learning Objective: 06-03 Use the sampling distribution of the sample proportion
 

Suppose that 60 percent of the student voters in a particular university support a candidate for students’ council president. Find the probability that a sample of 1,000 student voters would yield a sample proportion in favour of the candidate within:

 

Bowerman – Chapter 06
 

83. 4 percentage points of the actual proportion.

.9902

 

Bowerman – Chapter 06 #83
Difficulty: Hard
Learning Objective: N/A
 

84. 2 percentage points.

.8030

 

Bowerman – Chapter 06 #84
Difficulty: Hard
Learning Objective: N/A
 

85. Suppose you take a random sample of size n = 81 from a population with  = 1000 and   = 90. Find P(  > 1015).

0.0668

 

Bowerman – Chapter 06 #85
Difficulty: Medium
Learning Objective: N/A
 

A random sample of size 30 is taken from a population with mean 50 and standard deviation 5.

 

Bowerman – Chapter 06
 

86. Describe the shape of the sampling distribution of  .

Normal/approximately normal

 

Bowerman – Chapter 06 #86
Difficulty: Medium
Learning Objective: 06-02 Explain the central limit theorem
 

87. What is ?

50

 

Bowerman – Chapter 06 #87
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

88. What is ?

.913
 

Bowerman – Chapter 06 #88
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

89. Find P ( > 49).

.8643

 

Bowerman – Chapter 06 #89
Difficulty: Medium
Learning Objective: N/A
 

90. Find P ( < 48).

.0143

 

Bowerman – Chapter 06 #90
Difficulty: Medium
Learning Objective: N/A
 

91. Find P ( > 50.5).

.2912

 

Bowerman – Chapter 06 #91
Difficulty: Medium
Learning Objective: N/A
 

92. Find P ( < 51.5).

.95

 

Bowerman – Chapter 06 #92
Difficulty: Medium
Learning Objective: N/A
 

A random sample of size 1,000 is taken from a population where, for some characteristic of the population, p = .20.

 

Bowerman – Chapter 06
 

93. Describe the shape of the sampling distribution of  .

Normal/approximately normal

 

Bowerman – Chapter 06 #93
Difficulty: Medium
Learning Objective: 06-03 Use the sampling distribution of the sample proportion
 

94. What is ?

.20

 

Bowerman – Chapter 06 #94
Difficulty: Medium
Learning Objective: 06-03 Use the sampling distribution of the sample proportion
 

95. What is  ?

.01265

 

Bowerman – Chapter 06 #95
Difficulty: Medium
Learning Objective: 06-03 Use the sampling distribution of the sample proportion
 

96. Find P( < .18).

.0571

 

Bowerman – Chapter 06 #96
Difficulty: Medium
Learning Objective: N/A
 

97. Find P( > .175).

.9761

 

Bowerman – Chapter 06 #97
Difficulty: Medium
Learning Objective: N/A
 

98. Find P( > .21).

.2148

 

Bowerman – Chapter 06 #98
Difficulty: Medium
Learning Objective: N/A
 

99. Find P( < .22).

.9429

 

Bowerman – Chapter 06 #99
Difficulty: Medium
Learning Objective: N/A
 

100. Packages of sugar bags for Sweeter Sugar Inc. have an average weight of 16 grams and a standard deviation of 0.3 grams. The weights of the sugar bags are normally distributed. What is the probability that 9 randomly selected packages will have a weight in excess of 16.025 grams?

0.0062

 

Bowerman – Chapter 06 #100
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 cm and a standard deviation of 0.2 cm.

 

Bowerman – Chapter 06
 

101. What is the probability that randomly selected 4 sheets will have an average length of less than 29.9 cm long?

0.668

 

Bowerman – Chapter 06 #101
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

102. A sample of four metal sheets is randomly selected from a batch. What is the probability that the average length of a sheet is between 30.25 and 30.35 cm long?

0.0215

 

Bowerman – Chapter 06 #102
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

103. Suppose the standard deviation increases to 0.3 cm. What is the probability that average length of a steel sheet from a sample of 9 units is more than 29.95 cm long?

0.8413

 

Bowerman – Chapter 06 #103
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

The chief chemist for a major oil/gasoline production company claims that the regular unleaded gasoline produced by the company contains on average 4 grams of a certain ingredient. The chemist further states that the distribution of this ingredient per L of regular unleaded gasoline is normal and has a standard deviation of 1.2 grams.

 

Bowerman – Chapter 06
 

104. What is the probability of finding an average in excess of 4.3 grams of this ingredient from randomly inspected 100L of regular unleaded gasoline?

.0062

 

Bowerman – Chapter 06 #104
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

105. What is the probability of finding an average less than 3.85 grams of this ingredient from randomly inspected 64L of regular unleaded gasoline?

.1587

 

Bowerman – Chapter 06 #105
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

In the upcoming students’ council election, the most recent poll based on 900 students predicts that the incumbent will be re-elected with 55% of the votes.

 

Bowerman – Chapter 06
 

106. From the 900 students, how many indicated that they would not vote for the current students’ council president or indicated that they were undecided?

405
(.45)(900) = 405

 

Bowerman – Chapter 06 #106
Difficulty: Easy
Learning Objective: 06-03 Use the sampling distribution of the sample proportion
 

107. What is ?

.0166

 

Bowerman – Chapter 06 #107
Difficulty: Medium
Learning Objective: 06-03 Use the sampling distribution of the sample proportion
 

108. For the sake of argument, assume that 51% of the actual student voters in the university support the incumbent council president (p = 0.51). Calculate the probability of observing a sample proportion of voters 0.55 or higher supporting the incumbent council president.

.0082

 

Bowerman – Chapter 06 #108
Difficulty: Medium
Learning Objective: N/A
 

It has been reported that the average time to download the home page from a government website was 0.9 seconds. Suppose that the download times were normally distributed with a standard deviation of 0.3 seconds. If random samples of 36 download times are selected:

 

Bowerman – Chapter 06
 

109. Describe the shape of the sampling distribution. How was this determined?

Normal because the original population was normal.

 

Bowerman – Chapter 06 #109
Difficulty: Easy
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

110. Calculated the mean of the sampling distribution of the sampling mean.

0.9

= 0.9

 

Bowerman – Chapter 06 #110
Difficulty: Easy
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

111. Calculate the standard deviation of the sampling distribution of the sample mean.

0.05

=

 

Bowerman – Chapter 06 #111
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

112. 80% of the sample means will be between what two values symmetrically distributed around the population mean.

.83575, .96425
Z = ±1.285

1.285 =   , -1.285 =

 

Bowerman – Chapter 06 #112
Difficulty: Hard
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

113. What is the probability that the sample mean will be less than 0.80 seconds?

.0228

 

Bowerman – Chapter 06 #113
Difficulty: Hard
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

A standardized test has a   =3.5 and   =0.5. Suppose a random sample of 100 individual test scores is selected.

 

Bowerman – Chapter 06
 

114. What is  ?

= 3.5

 

Bowerman – Chapter 06 #114
Difficulty: Easy
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

115. Calculated  .

.05

=

 

Bowerman – Chapter 06 #115
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

116. Find the interval that contains 95.44% of the sample means.

3.4, 3.6
[3.5 ± 2(.05)] = (3.5 ± .1) = [3.4, 3.6]

 

Bowerman – Chapter 06 #116
Difficulty: Medium
Learning Objective: N/A
 

117. What is the probability that the random sample of 100 test scores have a mean greater than 3.65?

.0013

, .5 – .4987 = .0013

 

Bowerman – Chapter 06 #117
Difficulty: Medium
Learning Objective: N/A
 

The diameter of small toy balls manufactured at a factory is expected to be approximately normally distributed with a mean of 5.2 cm and a standard deviation of .08 cm. Suppose a random sample of 20 balls are selected.

 

Bowerman – Chapter 06
 

118. Calculate the mean of the sampling distribution of the sample mean.

 

 

Bowerman – Chapter 06 #118
Difficulty: Easy
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

119. Calculate the standard deviation of the sampling distribution of the sample mean.

.018

 

Bowerman – Chapter 06 #119
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

120. Find the interval that contains 95.44% of the sample means.

5.164, 5.236
[5.2 ± 2(.018)] = [5.2 ± .036] = 5.164, 5.236

 

Bowerman – Chapter 06 #120
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

121. What percentage of sample means will be less than 5.00 cm?

less than .01%

less than .01%

 

Bowerman – Chapter 06 #121
Difficulty: Medium
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean
 

122. The mean of the sampling distribution of the sample proportion  is equal to _____.

p

 

Bowerman – Chapter 06 #122
Difficulty: Medium
Learning Objective: 06-03 Use the sampling distribution of the sample proportion
 

 

 

c6 Summary

Category	# of Questions
Accessibility: Keyboard Navigation	25
Bowerman – Chapter 06	135
Difficulty: Easy	12
Difficulty: Hard	18
Difficulty: Medium	92
Learning Objective: 06-01 Demonstrate the sampling distribution of the sample mean	53
Learning Objective: 06-02 Explain the central limit theorem	10
Learning Objective: 06-03 Use the sampling distribution of the sample proportion	22
Learning Objective: N/A	36