Question

Assume that the salaries of elementary school teachers in the United States are normally distributed with a mean of $28,000 and a standard deviation of $3000.

What is the cutoff salary for teachers in the bottom 10%?

Answer 1

Let X be the salaries of elementary school teachers in the United States.

Given that, X follows Normal Distribution with parameters mean =$28000 and variance = $3000^2.

Also, we have given that,

P(X<=x) =.1

by standardizing the normal variate

P((X-mean)/S.D <=(x-mean)/S.D) =0.1 -------(1)

=>P(Z<=Z) = -------------------------------(2)

from (1) and (2) we have,

(x-28000)/3000 =Z

we know that Zalpha at left tail is -1.2816

x-28000 = -1.2816 * 3000  

x = 28000-1.2816*3000

x = 24155.2