Question

# 5. Supposing a company charges a premium of $150 per year for an insurance policy for storm damage to roofs.

Actuarial studies show that in case of a storm, the insurance company will pay out an average of $8000 for damage to a composition shingle roof and an average of $12,000 for damage to a shake roof. They also determine that out of every 10,000 policies, there are 7 claims per year made on composition shingle roofs and 11 claims per year made on shake roofs. What is the company's expected value (i.e., expected profit) per year of a storm insurance policy? What annual profit can the company expect if it issues 1000 such policies?

A) What is the probability of a composition shingle roof claim out of 10,000 = ______

B) What is the probability of a shake roof claim out of 10,000 = ______

C) How many claims are made out of 10,000? = _______

D) What is the probability of no claims out of 10,000? = _______

E) How much does each shingle roof claim cost the company, don't forget each person pays $150 for the insurance? = ______

F) How much does each shake roof claim cost the company? = _____

G) How much money does the company make from each customer that does not make a claim? = ______

H) What is the Expected Value (this time you have 2 values to subtract from the Profit in the formula.

I) Write formula used here_______________________________________________________

J) What is the company's Expected Value = _________

L) How much profits will the company makes if it issues 1000 such policies? = _______

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