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

Since n = 69 which is greater than 30, the population need not be normally distributed for the sampling distribution of sample means, 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 , = = 64

Standard deviation of , = = 0.4815