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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 0.02 cm.

If is the sample mean diameter for a random sample of n = 16 rings, where is the sampling distribution of centered?

Give answer to three decimal places. What is the standard deviation of the distribution of ?

Now suppose the sample size is n = 64 rings. Where is the sampling distribution of centered?

Give answer to four decimal places

Using the information from (c) above, what is the standard deviation of the distribution?

For which of the two random samples, the one from part (a) or the one from part (c), is more likely to be within 0.01 cm of 12 cm?

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