7.36 Paper Strength A manufacturer of paper used for packaging requires a minimum strength of 1400 g/cm. 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 or of the strength measure- ments, computed by pooling the sum of squares of deviations of many samples, is known to equal 140 g/cm, 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 1450 g/cm, what is the approximate probability that, for a random sample of n = 10 test pieces of paper, <1400?

c. What value would you select for the mean paper strength in order that P <1400) be equal to 0.001?