Question

Random samples with size 30 are drawn from the population with a mean of 25 and a standard deviation of 7. Find the mean and the standard error of the sample mean.

Answer 1

The mean of the sample means is the same as the mean of the population:

$E\bar{x}=30$

The standard error is

$\sigma \bar{x}=\frac{\sigma \left( X \right)}{\sqrt{n}}=\frac{7}{\sqrt{30}}$