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 16 cm and standard deviation 0.07 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 standard deviation (b) Answer the questions posed in part (a) for a sample size of n = 64 rings. center standard deviation (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 16 cm? Explain your reasoning. X is more likely to be within 0.01 cm of 16 cm in sample (a) because of the decreased variability with a smaller sample size. X is more likely to be within 0.01 cm of 16 cm in sample (b) because of the decreased variability with a larger sample size. X is more likely to be within 0.01 cm of 16 cm in sample (a) because of the increased variability with a maller sample size. X is more likely to be within 0.01 cm of 16 cm in sample (b) because of the in reased variability with a larger sample size.

Explanation / Answer

a)

By central limit, it has the same center,

center = u = 16 [ANSWER]

but a reduced standard deviation,

sigma(X) = sigma/sqrt(n) = 0.07/sqrt(16) = 0.0175 [ANSWER]

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b)

By central limit, it has the same center,

center = u = 16 [ANSWER]

but a reduced standard deviation,

sigma(X) = sigma/sqrt(n) = 0.07/sqrt(64) = 0.00875 [ANSWER]

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c)

As there is less variability in part B, then it will more probably be closer to the true mean,

OPTION B. [ANSWER]

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