Question: The idea of insurance is that we all face risks that are unlikely, but carry high costs – such as a fire destroying a home. An insurance company looks at the records for millions of homeowners and sees that the mean loss from fire in a year is $250 per house and the standard deviation is $1000. The company plans to sell fire insurance for $250 + their estimate of what it will take to cover their costs and profits.

a) What shape would we expect the distribution of losses per home to be? (Justify your answer)

b) Explain clearly why it would be unwise to sell only 12 policies.

c) If the company sells 10,000 policies, what is the probability that the average loss in a year will be greater than $275?