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.

1.    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?