A simple random sample of size n=35 is obtained from a population with =65 and =9. Does the population need to be normally distributed for

A simple random sample of size n=35 is obtained from a population with μ=65 and σ=9. Does the population need to be normally distributed for the sampling distribution of overbarx to be approximately normally distributed? Why? What is the sampling distribution of overbarx?

Does the population need to be normally distributed for the sampling distribution of overbarx to be approximately normally distributed? Why?

A. Yes because the Central Limit Theorem states that the sampling variability of nonnormal populations will increase as the sample size increases.

B. No because the Central Limit Theorem states that only if the shape of the underlying population is normal or uniform does the sampling distribution of overbarx become approximately normal as the sample size, n, increases.

C. Yes because the Central Limit Theorem states that only for underlying populations that are normal is the shape of the sampling distribution of overbarx normal, regardless of the sample size, n.

D. No because the Central Limit Theorem states that regardless of the shape of the underlying population, the sampling distribution of overbarx becomes approximately normal as the sample size, n, increases.

What is the sampling distribution of x overbarx?

Select the correct choice below and fill in the answer boxes within your choice.

(Type integers or decimals rounded to three decimal places as needed.)

A. The sampling distribution of overbarx is uniform with μoverbar=____ and σoverbarx=_____.

B. The sampling distribution of overbarx is normal or approximately normal with μoverbar=____ and σoverbarx=_____.

C. The sampling distribution of overbarx is skewed left with μoverbar=____ and σoverbarx=_____.

D. The sampling distribution of overbarx follows Student's t-distribution with μoverbar=____ and σoverbarx=_____.