The diameter of fiber optic cable wite harnesses supplying the telecommunications industry manufactured at a large factory in upstate New York is expected to be normally distributed with a mean of 1.30 inches and a standard deviation of 0.04 inches. The supplier is trying to verify an important product measure prior to shipment of a large order to a customer. If the true spec is significantly different from sample values, a decision may be made to hold up the order and examine it in more detail, delaying delivery.

What is the probability that a randomly selected wire harness will have a diameter of,

a. Between 1.28 and 1.30 inches?

b. Between 1.31 and 1.33 inches?

If random samples of 16 fiber optic wire harnesses were selected, what proportion of the sample means would be:

c. Between 1.28 and 1.30 inches?

d. Between 1.31 and 1.33 inches?

e. Compare your results in b) and (c).