A manufacturing representative is considering the option of taking out an insura

Question

A manufacturing representative is considering the option of taking out an insurance policy to cover possible losses incurred by marketing a new product. If the product is a complete failure, the representative feels that a loss of $80,000 would br incurred. If the profduct is only moderately successful, a loss of $25, 000would be incurred. Insurance companies have determined that the probablilities that the product will be a failure or only moderately successful are 0.01 and 0.05, respectively. The manufacturing representative is willing to ignore all other possible losses. If the insurance company charges $2,500 for the policy. What is the profit the insurance companu will male? Show all your work. Remeber to define a random variable for what you are trying to find.

Explanation / Answer

Let X be the random variable reperesnting the loss

Expected value of the loss, E[X] = 0.01 x 80000 + 0.05 x 25000 = $ 2050

So the insurance company will pay an expected amount of $ 2,050

Premium to be collected = $ 2,500

Expected profit = 2500 - 2050 = $ 450.

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