##### Question

In: Statistics and Probability

# Salaries for teachers in a particular elementary school district are normally distributed with a mean of...

Salaries for teachers in a particular elementary school district are normally distributed with a mean of $46,000 and a standard deviation of$4,500. We randomly survey ten teachers from that district. (Round your answers to the nearest dollar.)

A) Find the 90th percentile for an individual teacher's salary.

B)Find the 90th percentile for the average teacher's salary.

## Solutions

##### Expert Solution

Solution:

Given that,

mean = = 46,000

standard deviation = = 4,500

Using standard normal table,

a ) P(Z < z) = 90%

P(Z < z) = 0.90

P(Z < 1.28) = 0.27

z = 1.28

Using z-score formula,

x = z * + x = 1.28 * 4,500 + 46,000

x = 51760

The 90th percentile =51760

b )n = 10  = 46,000  = / n = 4,50010 =1423.0249

P(Z < z) = 90%

P(Z < z) = 0.90

P(Z < 1.28) = 0.27

z = 1.28

Using z-score formula, = z *  +   = 1.28 * 1423.0249 + 46,000 = 47821.47

The 90th percentile =47821

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