The length of a trout in a lake is known to have a highly skewed population dist

Question

The length of a trout in a lake is known to have a highly skewed population distribution with a mean of 10.2 inches and a standard deviation of 1.4 inches. suppose a random sample of 4 fish are taken from the lake. The sample distribution for the sample mean of 4 fish will be...

A) most likely skewed since the sample size is small and the population is not normal

B) normally distributed with a mean of 10.2 and a SD of .7

C) normally distributed with a mean of 10.2 and a SD of 1.4

D) highly skewed with a mean of 10.2 and a SD of 1.4

Explanation / Answer

According to the central limit theorem: no matter what population you start with, the sampling distribution of the sample mean is approximately normal if the sample size is large.

But here the sample size is small so from above we can say the sample distribution is not normal.

So ans is option-A.

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