The inside diameter of a randomly selected piston ring is a random variable with mean value 12 cm and standard deviation .04 cm.

a. If X is the sample mean diameter for a random sample of n = 16 rings, where is the sampling distribution of X centered, and what is the standard deviation of the X distribution?

b. Answer the questions posed in part

(a) for a sample size of n = 64 rings.

c. For which of the two random samples, the one of part

(a) or the one of part (b), is X more likely to be within.01 cm of 12 cm? Explain your reasoning.