Answer to Question #129162 in Statistics and Probability for paola

Question

10. 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 $4000. What is the cutoff salary for teachers in the top 10%?

Answer 1

The mean is $32,00 and a standard deviation of $4,000

To get the z-score from which the top 10% start, we use the sketch below and and the standard normal distribution tables.

We use the formula z=$\frac{X-\mu}{\sigma}$

z = 1.2816 = $\frac{X- 32,000}{4,000}$

X = (1.2816*$4,000) + $32,000

X = $37,126.40

Therefore, the cutoff salary for teachers in the top 10% is $37,126.40