The inside diameter of a randomly selected piston ring is a random variable with mean value 12 cm and standard deviation 0.04 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 question 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.

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