Question

A simple random sample of size

nequals=6969

is obtained from a population with

muμequals=6464

and

sigmaσequals=44.

Does the population need to be normally distributed for the sampling distribution of

x overbarx

to be approximately normally​ distributed? Why? What is the sampling distribution of x bar?

What is the sampling distribution of

x overbarx​?

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

Answer 1

Given:

n = 69

64

= 4

Since n = 69 which is greater than 30, the population need not be normally distributed for the sampling distribution of sample means, $\bar{X}$ to be approximately normally distributed

(From Central Limit Theorem, the sampling distribution of sample means is approximately normally distributed if the sample size is greater than 30)

Mean of $\bar{X}$,
L
= $\mu$ = 64

Standard deviation of $\bar{X}$, $\sigma_{\bar{X}}$ = $\frac{\sigma}{\sqrt{n}}$ = 0.4815