Question

A certain population has a mean of 450 and a standard deviation of 25. Many samples of size 60 are randomly selected and the means calculated.

(a) What value would you expect to find for the mean of all these sample means? (Give your answer correct to nearest whole number.)

(b) What value would you expect to find for the standard deviation of all these sample means? (Give your answer correct to two decimal places.)

Answer 1

Solution :

Given that ,

mean = $\mu$ = 450

standard deviation = $\sigma$ = 25

n = 60

(a )$\mu$_{$\bar x$} = 450

(b )$\sigma$_{$\bar x$} = $\sigma$ / $\sqrt$n = 25 / $\sqrt$60 = 3.23