Question

A random sample of size 14 was taken from a normally distributed population with a population mean 25 and a population standard deviation 6.

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 normal? Yes or No

Answer 1

Solution :

Given that ,

mean = = 25

standard deviation = = 6

n = 14

a) = = 25

b) = / n = 6 / 14 = 1.604

c) The distribution of sample means will be approximately normal as long as the sample size is large enough. We will depend on the Central Limit Theorem again and again in order to do normal probability calculations when we use sample means to draw conclusions about a population mean