Question

Suppose that a random sample of size 64 is to be selected from a population with mean 40 and standard deviation 5. (a) what are the mean and standard deviation of the x sampling distribution?

Answer 1

The sample mean is equal to the population mean.
$\bar{X}=\mu=40$
The standard deviation of X-bar (the standard error) is:
$S.E.=\frac{\sigma}{ \sqrt{n} }=\frac{5}{\sqrt{64}}=0.625$