.A life insurance company sells a policy which pays $100,000 in case of death.The policy also pays hospital bills in case of injury.These bills average $50,000 with a standard deviation of $10,000.In any particular month there is a 5% chance of a death claim.Injury claims follow a Poisson distribution with an average of two claims per month.

The company wants to estimate the total dollar amount of claims paid out each month to determine the minimum insurance premium it must charge customers to remain profitable.

Run 1000 simulations and answer the following questions:

a.Find the expected total claims paid out per month.

b.Find the standard deviation of claims paid per month

c.What is the probability that the amount of claims exceed $200,000 in any month?

d.What is the probability the claims exceed $300,000 in any month?