2. The inside diameter of a randomly selected piston ring is a random variable following normal distribution with mean value 12 cm and standard deviation 0.04 cm. (a) If 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 posted 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 0.01 cm of 12 cm? Explain your reasoning.