Question

Assume that the salaries of elementary school teachers in a particular country are normally distributed with a mean of $38,000 and a standard deviation of $4,000. What is the cutoff salary for teachers in the top 7%?

Answer 1

Answer:

$43,920.

Step-by-step explanation:

We have been given that the salaries of elementary school teachers in a particular country are normally distributed with a mean of $38,000 and a standard deviation of $4,000.

We will use the normal distribution table to solve our given problem. From normal distribution table, we need to find the z-score corresponding to the top 7% or z-score corresponding to probability 93% (0.93).

From normal distribution table, we get our required z-score as 1.48.

Now, we will use z-score formula to solve for sample score as:

$z=\frac{x-\mu}{\sigma}\\\\1.48=\frac{x-38000}{4000}$

$1.48*4000=\frac{x-38000}{4000}*4000$

$5920=x-38000$

$5920+38000=x-38000+38000$

$43920=x$

Therefore, the cutoff salary for teachers in the top 7% is $43,920.