Statistics standard deviation

Question

Employees at XYZ company work at an average of 55 hours per week with the standard deviation of 9 hours. Promotions are more likely for those employees in the upper 10% of the time they spend working. How long must an employee work to increase his chances of promotion ?​

Answer 1

We want to find the number of hours x for the 90th percentile.

Find the z-score corresponding to the 90th percentile = 1.28

We will use the formula:

z = (x - mean)/SD, where z is 1.28, mean is 55 and SD is 9.

1.28 = (x - 55)/9

x = 1.28 * 9 + 55 = 66.52