A manufacturer of paper employed for packaging needs a minimum strength of 20 pounds per square inch. To check on the quality of paper, a random sample of ten pieces of paper is chosen each and every hour from the previous hour's production and a strength measurement is recorded for each. The standard deviations of strength measurements, calculated by pooling the sum of squares of deviations of many samples, is known to equal 2 pounds per square inch.
a) Determine the approximate probability distribution of the sample mean n=10 test pieces of paper?
b) If the mean of population of strength measurements is 21 pounds per square inch, determine the approximate probability that,for a random sample of n=10 test pieces of paper, x<20?