Question

Records of a company show that 20% of the employees have only a high school diploma; 70% have bachelor degrees; and 10% have graduate degrees. Of those with only a high school diploma, 10% hold management positions; whereas, of those having bachelor degrees, 60% hold management positions. Finally, 85% of the employees who have graduate degrees hold management positions. What percentage of employees hold management positions?

Answer 1

62.5% of employees hold management positions

Explanation:

We have these following percentages:

20% of the employees have only a high school diploma;

70% have bachelor degrees;

10% have graduate degrees;

Of those with only a high school diploma, 10% hold management positions;

Of those having bachelor degrees, 60% hold management positions;

85% of the employees who have graduate degrees hold management positions

What percentage of employees hold management positions?

That is

`P = P_(1) + P_(2) + P_(3)`.

In which
`P_(1)` is the percentage of those who only have a high school diploma and hold a management position. So
`P_(1) = 0.2*0.1 = 0.02`

`P_(2)` are those who have a bachelor degree and hold a management position. So
`P_(2) = 0.7*0.6 = 0.52`.

`P_(3)` are those who have a graduate degree and hold a management position. So
`P_(3) = 0.1*0.85 = 0.085`

Finally

`P = P_(1) + P_(2) + P_(3) = 0.02 + 0.52 + 0.085 = 0.625`.

62.5% of employees hold management positions