Quality control. Refer to Exercise 6.64. The mean diameter of the bearings produced by the… 1 answer below »

Quality control. Refer to Exercise 6.64. The mean diameter of the bearings produced by the machine is supposed to be .5 inch. The company decides to use the sample mean from Exercise 6.64 to decide whether the process is in control (i.e., whether it is producing bearings with a mean diameter of .5 inch). The machine will be considered out of control if the mean of the sample of n = 25 diameters is less than .4994 inch or larger than .5006 inch. If the true mean diameter of the bearings produced by the machine is .501 inch, what is the approximate probability that the test will imply that the process is out of control?
Exercise 6.64
Producing machine bearings. To determine whether a metal lathe that produces machine bearings is properly adjusted, a random sample of 25 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 .001 inch, what is the approximate probability that the mean diameter  of the sample of 25 bearings will lie within .0001 inch of the population mean diameter of the bearings?
b. If the population of diameters has an extremely skewed distribution, how will your approximation in part a be affected?