To determine whether a metal lathe that produces machine bearing is properly adjusted, a random sample of 36 bearings is collected and the diameter of each is measured.
a). If the standard deviation of the diameters of the bearings measured over a long period of time is 0.001 inch, what is the approximate probability that the mean diameter of the sample of 36 bearings will lie within 0.0001 inch of the population mean diameter of the bearings?
b) If the population of the diameters has a skewed distribution, how will your approximation in part (a) be affected?