A variable of a population has a mean of $\mu = 150$ and a standard deviation of $\sigma= 35$.

a. The sampling distribution of the sample mean for samples of size 49 is approximately normally distributed with mean and standard deviation .

b. For part (a) to be true, what assumption did you make about the distribution of the variable under consideration?

A. Normal distribution.
B. No assumption was made.
C. Uniform distribution.

c. Is the statement in part (a) still true if the sample size is 16 instead of 49? Why or why not?

A. Yes, the sampling distribution of the sample mean is always normal.
B. No. Because the distribution of the variable under consideration is not specified, a sample size of at least 30 is needed for part (a) to be true.
C. No, the sampling distribution of the sample mean is never normal for sample size less than 30.