SOLUTION: Suppose you set insurance prices for an insurance company. The insured object is a Dutch oven. With probability 0.02 the lid will need to be replaced and it will cost $50, with pro

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Question 1115295: Suppose you set insurance prices for an insurance company. The insured object is a Dutch oven. With probability 0.02 the lid will need to be replaced and it will cost $50, with probability 0.01 the pot will need to be replaced and it will cost $200. Your boss wants the insurance policy to generate $9 of expected profit.What should be the price of the insurance policy?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
you want eache policy to generate 9 dollars of profit.

there is one policy per pot.

your formula is:

9 = x - .02 * 50 - .01 * 200.

9 is the expected value
x is the price of the policy

solve for x to get x = 9 + .02 * 50 + .01 * 200 = 12 dollars

you would charge 12 dollars for each insurance policy.

suppose 1000 pots were insured.

that means you get 12 * 1000 = 12000 dollars.

.02 * 1000 pots require a new lid.

that means 20 pots need a lid for a total cost of 20 * 50 = 1000 dollars.

.01 * 1000 pots need to be replaced.

that means 10 pots need to be replaced for a total of 10 * 200 = 2000 dollars.

total cost to you for the 1000 insurance policies is 3000 dollars.

your profit is 12000 - 3000 = 9000 dollars.

divide that by 1000 insurance policies sold and your profit is 9 dollars per insurance policy sold.