Suppose a company charges a premium of $150 per year for an insurance policy for
ID: 446754 • Letter: S
Question
Suppose 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?
Determine the probability of a composition shingle roof claim out of 10,000 = ______
Determine the probability of a shake roof claim out of 10,000 = ______
How many claims are made out of 10,000? = _______
What is the probability of no claims out of 10,000? = _______
How much does each shingle roof claim cost the company, don’t forget each person pays $150 for the insurance? = ______
How much does each shake roof claim cost the company? = _____
How much money does the company make from each customer that does not make a claim? = ______
Calculate the Expected Value (this time you have 2 values to subtract from the Profit in the formula. Write formula used here_______________________________________________________
What is the company’s Expected Value = _________
How much profits will the company makes if it issues 1000 such policies? = _______
Explanation / Answer
on 1000 polocies company earns 150000 dollars(150*1000)
no. of claims for single roof will be 0.7 claims( considering 7 claims in every 10000 policies) out of 1000 policies costing 5600 dollars
no. of claims for shake proof will be 1.1 laims( considerin 11 claims in every 10000 claims) out of 1000 clais costing 13200 dollars
total payout on claims will be 18800 dollars hence profit will be 150000-18800= 131200 dollars
total claims made out of 10000 policies would be 18 hence total no claims would be 9982 company will make 149.78 dollars on average from each policy after claims payout.
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