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.

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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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.
Transcribed Image Text: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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