81. A design engineer wants to construct a sample mean chart for controlling the service life of a halogen headlamp his company produces. He knows from numerous previous samples that this service life is normally distributed with a mean of 500 hours and a standard deviation of 20 hours. On three recent production batches, he tested service life on random samples of four headlamps, with these results:

What is the mean of the sampling distribution of sample means when service life is in control?

A. 250 hours

B. 470 hours

C. 495 hours

D. 500 hours

E. 515 hours

82. A design engineer wants to construct a sample mean chart for controlling the service life of a halogen headlamp his company produces. He knows from numerous previous samples that this service life is normally distributed with a mean of 500 hours and a standard deviation of 20 hours. On three recent production batches, he tested service life on random samples of four headlamps, with these results:

What is the standard deviation of the sampling distribution of sample means for whenever service life is in control?

A. 5 hours

B. 6.67 hours

C. 10 hours

D. 11.55 hours

E. 20 hours

83. A design engineer wants to construct a sample mean chart for controlling the service life of a halogen headlamp his company produces. He knows from numerous previous samples that this service life is normally distributed with a mean of 500 hours and a standard deviation of 20 hours. On three recent production batches, he tested service life on random samples of four headlamps, with these results:

If he uses upper and lower control limits of 520 and 480 hours, what is his risk (alpha) of concluding that service life is out of control when it is actually under control (Type I error)?

A. 0.0026

B. 0.0456

C. 0.3174

D. 0.6826

E. 0.9544

84. A design engineer wants to construct a sample mean chart for controlling the service life of a halogen headlamp his company produces. He knows from numerous previous samples that this service life is normally distributed with a mean of 500 hours and a standard deviation of 20 hours. On three recent production batches, he tested service life on random samples of four headlamps, with these results:

If he uses upper and lower control limits of 520 and 480 hours, on what sample(s) (if any) does service life appear to be out of control?

A. sample 1

B. sample 2

C. sample 3

D. both samples 2 and 3

E. all samples are in control

85. A quality analyst wants to construct a sample mean chart for controlling a packaging process. He knows from past experience that whenever this process is under control, package weight is normally distributed with a mean of 20 ounces and a standard deviation of two ounces. Each day last week, he randomly selected four packages and weighed each:

What is the sample mean package weight for Thursday?

A. 19 ounces

B. 20 ounces

C. 20.6 ounces

D. 21 ounces

E. 23 ounces

86. A quality analyst wants to construct a sample mean chart for controlling a packaging process. He knows from past experience that whenever this process is under control, package weight is normally distributed with a mean of 20 ounces and a standard deviation of two ounces. Each day last week, he randomly selected four packages and weighed each:

What is the mean of the sampling distribution of sample means when this process is under control?

A. 18 ounces

B. 19 ounces

C. 20 ounces

D. 21 ounces

E. 22 ounces

87. A quality analyst wants to construct a sample mean chart for controlling a packaging process. He knows from past experience that whenever this process is under control, package weight is normally distributed with a mean of 20 ounces and a standard deviation of two ounces. Each day last week, he randomly selected four packages and weighed each:

What is the standard deviation of the sampling distribution of sample means for whenever this process is under control?

A. 0.1 ounces

B. 0.4 ounces

C. 0.5 ounces

D. 1 ounce

E. 2 ounces

88. A quality analyst wants to construct a sample mean chart for controlling a packaging process. He knows from past experience that whenever this process is under control, package weight is normally distributed with a mean of 20 ounces and a standard deviation of two ounces. Each day last week, he randomly selected four packages and weighed each:

If he uses upper and lower control limits of 22 and 18 ounces, what is his risk (alpha) of concluding this process is out of control when it is actually in control (Type I error)?

A. 0.0026

B. 0.0456

C. 0.3174

D. 0.6826

E. 0.9544

89. A quality analyst wants to construct a sample mean chart for controlling a packaging process. He knows from past experience that whenever this process is under control, package weight is normally distributed with a mean of 20 ounces and a standard deviation of two ounces. Each day last week, he randomly selected four packages and weighed each:

If he uses upper and lower control limits of 22 and 18 ounces, on what day(s), if any, does this process appear to be out of control?

A. Monday

B. Tuesday

C. Monday and Tuesday

D. Monday, Tuesday, and Thursday

E. none

90. A quality analyst wants to construct a control chart for determining whether three machines, all producing the same product, are under control with regard to a particular quality variable. Accordingly, he sampled four units of output from each machine, with the following results:

What is the sample mean for machine #1?

A. 15

B. 16

C. 17

D. 21

E. 23

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