Claims arrive at random times to an insurance company where you work as

branch manager. The daily amount of claims is normally distributed with a mean

of $1570 and standard deviation $450. Total claims on different days each has

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.

Please help me answer these questions. Do not upload in a handwritten format. I need clear explanation. Thank you