4 A manufacturer of paper used for packaging requires a mini

4. A manufacturer of paper used for packaging requires a minimum strength of 20 pounds
per square inch. To check the quality of the paper, a random sample of ten pieces of
paper is selected each hour from the previous hour\'s production and a strength
measurement is recorded for each. The distribution of strengths is known to be normal
and the standard deviation, computed from many samples, is known to equal 2 pounds
per square inch. The mean is known to be 21 pounds per square inch.
A. What are the mean and standard deviation of the sampling distribution for
n = 10?

B. What\'s the shape of the sampling distribution for n = 10?

C. Draw a random sample of size 10 from this distribution and compute the mean
of the sample, using the randNorm function on your calculator. Write down all your sample values. What are the mean and sample standard
deviation of this sample? Compare them with the mean and standard deviation of the parent population, and explain why they\'re different or the same.

D. Using the mean and standard deviation of the sampling distribution (from part A), calculate the probability of getting a sample mean less than what you got. If you use a calculator, show what you entered.

Solution

A. What are the mean and standard deviation of the sampling distribution for
n = 10?

mean=21

standard deviation =s/vn

= 2/sqrt(10)

=0.6324555

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B. What\'s the shape of the sampling distribution for n = 10?

bell shape

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C. Draw a random sample of size 10 from this distribution and compute the mean
of the sample, using the randNorm function on your calculator. Write down all your sample values. What are the mean and sample standard deviation of this sample? Compare them with the mean and standard deviation of the parent population, and explain why they\'re different or the same.

mean=21

standard deviation =0.6324555

The mean and standard deviation stay the same.

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D. Using the mean and standard deviation of the sampling distribution (from part A), calculate the probability of getting a sample mean less than what you got. If you use a calculator, show what you entered.

The probability is P(xbar<21)=P((xbar-mean)/s<(21-21)/0.6324555)=0 (from standard normal table)