The diameter of a brand of tennis balls is approximately normally distributed, w

Question

The diameter of a brand of tennis balls is approximately normally distributed, with a mean of 2.64 inches and a standard deviation of 0.04 inch. A random sample of 10 tennis balls is selected. Complete parts (a) through (d) below.

a. What is the sampling distribution of the mean? Which answer

A. Because the population diameter of tennis balls is approximately normally distributed, the sampling distribution of samples of size 10 will be the uniform distribution.

B. Because the population diameter of tennis balls is approximately normally distributed, the sampling distribution of samples of size 10 will not be approximately normal.

C. Because the population diameter of tennis balls is approximately normally distributed, the sampling distribution of samples of size 10 will also be approximately normal.

D. Because the population diameter of tennis balls is approximately normally distributed, the sampling distribution of samples of size 10 cannot be found.

Explanation / Answer

As per central limit theorem, if the population is normal distribution of sample mean is also normal even if sample size is smaller than 10.

So answer is

C. Because the population diameter of tennis balls is approximately normally distributed, the sampling distribution of samples of size 10 will also be approximately normal.

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