Claims arrive at random times to an insurance company. The daily amount of claims is normally distributed with mean $1570 and standard deviation $450. Total claims on different days each have this distribution, and they are probabilistically independent of one another.
a. Find the probability that the amount of total claims over a period of 100 days is at least $150,000.
b. If the company receives premiums totaling $165,000, find the probability that the company will net at least $10,000 for the 100-day period.