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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 year'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.

Sagot :

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Answer:

A.)

Mean, μ of sampling distribution = 21 pounds per square inch

Standard deviation of sampling distribution, s =

Step-by-step explanation:

Since the distribution is normal ;

Mean of sampling distribution = μ = 21 pounds per square inch

Standard deviation of sampling distribution, s = σ/sqrt(n)

σ = 2, n = 10

2 / sqrt(10)

2 / 3.1622776

= 0.632

B.) shape of distribution for n = 10 will be approximately normal.

C.)

{-7.22870249054, 40.8079452872, -10.91517422664,22.86455836927,32.94723256068,-5.93493872489,-6.11103290664,-5.04925181642,-27.62798560898,9.77607593874)

Mean = 4.35 ; Standard deviation = 21.6

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