The annual commissions per salesperson employed by a manufacturer of light machinery averaged $40,000 with a standard deviation of $5,000. What percent of the sales persons earn between $32,000 and $42,000?

60.06%

Explanation:

For each of the amounts first of all we get the z values.

For $32,000 z = (Amount - Mean) / Standard deviation

z = (32,000 - 40,000) / 5,000 = - 1.6

For $42,000, z = (42,000 - 40,000) / 5,000

z = 0.4

Using probability tables to find the proportion of commission between 0.4 and - 1.6, we will need to add 0.4452 and 0.1554.

This gives 0.6006 = 60.06%

So the salesperson earns 60.06% commission between $32,000 and $42,000.