Let the distribution of piston ring diameter be as before, with mean value 15 cm and standard deviation of 0.1 cm. Assume we are taking a sample of n piston rings, and that each ring's diameter is distributed independently of all others. Let X}, = $21.12, X,- be the sample average for a sample of size n. a.) If n = 9, what will the mean and standard deviation of X}, be? What, if anything, can we say about its distribution? b.) Repeat part a), but now with a sample size n = 400. 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 .005 cm of 15 cm? Explain your reasoning. (Calculating the exact probability is not necessary)