29. Paper Strength A paper manufacturer 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. Assume that the strength measurements are normally distributed with a standard deviation s 5 2 pounds per square inch.

a. What is the approximate sampling distribution of the sample mean of n510 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 5 10 test pieces of paper, x , 20?

c. What value would you select for the mean paper strength m in order that P(x , 20) be equal to .001?