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%

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()

The standard normal z score distribution is given by;

          Z = ~ 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( < ) = 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% .

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step-by-step explanation: