Suppose the distribution of the daily calcium intake of Amer

Suppose the distribution of the daily calcium intake of Americans is left skewed with a mean of 800 mg and a standard deviation of 16 mg. What can we say about the sampling distribution of distribution X?
a. The mean of the sampling distribution of X is 800.

b.The standard deviation of the sampling distribution of X is 16.

c.The value of every sample mean is 800The sampling distribution of X will be approximately normal regardless of sample size.

d.Exactly 2 of the above are correct.

Solution

A is true by central limit theorem. The sampling distribution will have the same mean as the original distribution.

B is false. The sampling distribution will have a standard deviation of s/sqrt(n), so it cannot be a fixed 16.

C is false. The normal approximation improves with increasing sample size.

So, the answer is OPTION A. [answer, A]