Chapter 7, Problem 26PS

An industrial sewing machine uses ball bearings that are targeted to have a diameter of 0.75 inch. The lower upper specification limits under which the ball bearing can operate are 0.74 inch (lower) and 0.76 inch (upper). Past experience has indicated that the actual diameter of the ball bearings is approximately normally distributed, with a mean of 0.753 inch and a standard deviation of 0.004 inch. If you select a random sample of 25 ball bearings, what is the probability that the sample mean is

a. between the target and the population mean of 0.753?

b. between the lower specification limit and the target?

c. greater than the upper specification limit?

d. less than the lower specification limit?

e. The probability is $93\%$ that the sample mean diameter will be greater than what value?