based on insurance company's past data

Question

Based on an insurance company's past data, each year an average of 1/25 policy holders make a claim of $500, 1/100 policy holders make a claim of $12,000, and 1/400 policy holders make a claim of $17,000.

• What would the insurance company have to charge per policy holder to break even? In other words, what would the premium have to be in order to make the expected value of the policy zero? (Round to the nearest dollar.)

• If the company sells insurance policies for $300 annually, what is the expected profit or loss for the company per policy holder over the course of a year? (Round to the nearest dollar.)

 

• If the company sold 650 policies, what would the overall expected profit or loss be? (Use your unrounded answer from the previous question to calculate this.) (Round to the nearest dollar.)

Answer 1

E(X) = 0 = P -500(0.04)-12,000(0.01)-17,000(0.0025),

if each customer pays a premium P, and 4% of them file claims $500, etc.

 

Therefore P = _____  You do this work & use it as basis for answering other parts