Question

An alumni association of a major university finds that 30% of its members attained advanced degrees, 50% attained a bachelor's degree, and 20% did not graduate.

The mean income of a graduate with an advanced degree is $75,000, the mean income of a graduate with a bachelor's degree is $54,000, and the mean income of a student that did not graduate is $36,000.
From past results, alumni members donate 5% of their income to the university. If 50 members of the alumni association are randomly selected, what is the expected total donation?
a. $2,750.
b.$2,835.
c.$135,000.
d.$137,500.
e.$141,750.

Answer 1

e)$141,750

Explanation:

Let be

AG = Members with advanced degrees

BG = Members with a bachelor's degree

DG = Members with a no degree

In a sample of 50 members it is expected a total of members for every group as follows

For AG = 30 * 0.5 = 15

For BG = 50 * 0.5 = 25

For DG = 20 * 0.5 = 10

The expected donation for every group would be the number of members by the 5% of their incomes

For AG = 15 * 0.05 * $75,000 = $56,250

B For G = 25 * 0.05 * $54,000 = $67,500

For DG = 20 * 0.05 * $36,000 = $18,000

Total donation is the sum = $141,750