Question

A sample of 100 people was taken from a population that has mean 40 and standard deviation 15. Use the CLT to give the mean and sampling distribution of Xbar.

Answer 1

Solution :

using central limit theorem

Given that ,

mean = $\mu$ = 40

standard deviation = $\sigma$ = 15

n = 100

sample distribution of sample mean is ,

$\mu$$\bar x$ = $\mu$

$\mu$$\bar x$ = 40

sampling distribution of standard deviation

$\sigma$$\bar x$ =$\sigma$  / $\sqrt$ n = 15/ $\sqrt$ 100=1.5

$\sigma$$\bar x$ = 1.5