Normal Distribution:

An industry sewing machine uses ball bearings that are targeted to have a diameter of 0.75 inch. The lower and 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 bearing is approximately normally distributed with a mean of 0.754 inch and a standard deviation of 0.004inch.

If you select a random sample of 25 ball bearings, what is the probability that the sample mean is:

(a) What is the probability that a ball bearing has a diameter great than the upper specification limit? (b) What is the probability that a ball bearing has a diameter lower than the lower specification limit? (c) The probability is 93% that the diameter of the ball bearing will be greater than what value? If you select a random sample of 25 ball bearings, what is the probability that the sample mean is: (d) between the target and the population mean? (e) between the lower specification limit and the target? (f) greater than the upper specification limit (g) For the same sample of 25 ball bearings, the probability is 93% that the sample mean diameter will be greater than what value?