Question

The mean salary of public school teachers in the United States in 2012 was $50,547 with a standard deviation of $9,000. Assume these salaries are normally distributed. Find the percentage of public school teachers who earn less than $32,547. 13.5% 2.5% 68% 95%

Answer 1

Answer:

Percentage of public school teachers who earn less than $32,547 = 2.3%

Step-by-step explanation:

We are given that the mean salary of public school teachers in the United States in 2012 was $50,547 with a standard deviation of $9,000. Also, salaries are normally distributed.

Let X = Salary of public school teachers

So, X ~ N($\mu = 50,547 , \sigma^{2} = 9000^{2}$)

The standard normal z score distribution is given by;

          Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

So, percentage of public school teachers who earn less than $32,547 is given by = P(X < $32,547)

P(X < 32,547) = P( $\frac{X-\mu}{\sigma}$ < $\frac{32,547-50,547}{9000}$ ) = P(Z < -2) = 1 - P(Z <= 2)

                                                               = 1 - 0.97725 = 0.02275 or 2.3%

Therefore, percentage of public school teachers who earn less than $32,547 is 2.3% .