Answer to Question #292296 in Statistics and Probability for Yaku

Question

7. A manufacturer of paper used for packaging requires a minimum strength of 20 pounds per square inch. To check on the quality of the paper, a random sample of 10 pieces of paper is selected each hour from the previous hour's production and a strength measurement is recorded for each. The standard deviation $\sigma$ of the strength measurements, computed by pooling the sum of squares of deviations of many samples, is known to equal 2 pounds per square inch, and the strength measurements are normally distributed.

a) What is the approximate sampling distribution of the sample mean of n = 10 test pieces of paper?

b) If the mean of the population of strength measurements is 21 pounds per square inch, what is the approximate probability that, for a random sample of n = 10 test pieces of paper, X \bar < 20?

c) What value would you select for the mean paper strength in order that P( X \bar < 20) be equal to 0.001?