Question

A random sample of size 137 was taken from a population with a population mean 25 and a population standard deviation 5.

Determine each of the following about the sampling distribution of the sample mean.

Round your answer to at least 3 decimal places where appropriate.

a) μx_=   

b) σx_=   

c)  Can we conclude that the sampling distribution of the sample mean is approximately normal?      YesNoClick for List  

Answer 1

Solution :

Given that,

mean = $\mu$ = 25

standard deviation = $\sigma$ = 5

n = 137

The sampling distribution of mean and standard deviation is ,

a)

$\mu$_{$\bar x$} = 25

b)

$\sigma$_{$\bar x$} = $\sigma$ / $\sqrt$ n = 5 / $\sqrt$ 137 = 0.427

c)

yes