A close friend of mine became very ill and couldn’t work for several months. Nat

Question

A close friend of mine became very ill and couldn’t work for several months. Naturally, this put a big strain on his family financially. I decided to start a GoFundMe page to help with his medical costs. After some research, I found that donations for a GoFundMe for this type of situation are normally distributed with a mean of $100 and a standard deviation of $60. I was able to reach almost 5,000 people, and actually received contributions from 2,550 of them. Let S be the aggregate donations given by the 2,550 individuals.

a) What is the mean, variance, and standard deviation of the aggregate donation, S?

b) What is the probability that the aggregate donation, S, exceeds $260,000?

Explanation / Answer

Solution:

a. The mean of the aggregate donation, S = nµ

Mean = 2550 (100)

Mean = 255000

Variance = (SD)^2*n

Variance = (60)^2*2550

Variance = 9180000

Standard deviation = sqrt (variance)

Standard deviation = sqrt(9180000)

Standard deviation = 3029.85

b. The respective Z-score with X = 260,000 is

Z = (X - mean)/SD

Z = (260,000 - 255,000)/3029.85

Z = 1.65

Using Z-tables, the probability is

P [Z > 1.65] = 1 - 0.95 = 0.05

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.