The inside diameter of a randomly selected piston ring is a random variable with

Question

The inside diameter of a randomly selected piston ring is a random variable with mean value 9 cm and standard deviation 0.06 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 cm
standard deviation 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 cm
standard deviation cm

Explanation / Answer

a) ANSWER: Sampling Distribution Mean = 12cm, Sampling Distribution Standard Deviation = 0.01cm Why?? Central Limit Theorem states that Sampling Distributions are always normal irregardless of the underlying distribution. Sampling Distribution Standard Deviation = Population Standard Deviation/SQRT(Sample Size) [0.04/SQRT(16)] b) ANSWER: Sampling Distribution Mean = 12cm, Sampling Distribution Standard Deviation = 0.01 due to the 1/SQRT(Sample Size) multiplying factor.

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