Question

Assume that the salaries of elementary school teachers in the unaired states have a mean of $32,000 and a standard deviation of $3000. if 100 teachers are randomly selected, would it be unusual to obtain a sample mean of 32450? answer by calculating the appropriate z-score.

Answer 1

Solution :

Given that ,

mean = $\mu$ = 32000

standard deviation = $\sigma$ = 3000

n = 100

$\mu$_{$\bar x$} = 32000

$\sigma$_{$\bar x$} =$\sigma$  / $\sqrt$ n = 3000 / $\sqrt$ 100=300

$\bar x$ =32450

using z score formula

z=($\bar x$ - $\mu$ _{$\bar x$} ) / $\sigma$ _{$\bar x$}

= 32450-32000/300

=1.5

z score =1.5