Question

Assume that the salaries of elementary school teachers in the United States are normally distributed with a mean of $32,000 and a standard deviation of $3000. If 100 teachers are randomly selected, find the probability that their mean salary is greater than $32,500.

Answer 1

Given,

$\mu$ = 32000 , $\sigma$ = 3000

Using central limit theorem,

P($\bar{x}$ < x) = P(Z < ( x - $\mu$ ) / ($\sigma$ / sqrt(n) ) )

So,

P($\bar{x}$ > 32500) P(Z > (32500 - 32000) / (3000 / sqrt(100) ) )

= P(Z >1.67)

= 0.0475