MY NOTES ASK YOUR TEACHER The inside diameter of a randomly selected piston ring is a random variable with mean value 9 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? (Enter your standard deviation to five decimal places.) center 8 x cm standard deviation .01 cm (b) Answer the questions posed in part (a) for a sample size of n = 64 rings. (Enter your standard deviation to five decimal places.) center 12 x cm standard deviation .005 cm (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 9 cm? Explain your reasoning. O X is more likely to be within 0.01 cm of 9 cm in sample (b) because of the increased variability with a larger sample size. O X is more likely to be within 0.01 cm of 9 cm in sample (a) because of the increased variability with a smaller sample size. O X is more likely to be within 0.01 cm of 9 cm in sample (b) because of the decreased variability with a larger sample size. O X is more likely to be within 0.01 cm of 9 cm in sample (a) because of the decreased variability with a smaller sample size. 5 2 APR 1 3 W O