Question

The idea of insurance is that we all face risks that are unlikely but carry high cost. Think of a fire destroying your home. Insurance spreads the risk: we all pay a small amount, and the insurance policy pays a large amount to those few of us whose homes burn down. An insurance company looks at the records for millions of homeowners and sees that the mean loss from fire in a year is μ = $250 per person. (Most of us have no loss, but a few lose their homes. The $250 is the average loss.) The company plans to sell fire insurance for $250 plus enough to cover its costs and profit.

Why is it that selling thousands of such policies is a safe business?

• Because for thousands of policies, the law of large numbers implies that the average claim on many policies will be close to the mean.
• Because for thousands of policies, the law of large numbers implies that the average claim on many policies will be larger than the mean.
• The statement is wrong. It is not wise to sell thousands of such policies, since this will result in a large number of claims.
• Because for thousands of policies, the law of large numbers implies that the average claim on many policies will be smaller then the mean.

Answer 1

Selling thousands of policies is wise Because for thousands of policies, the law of large numbers implies that the average claim on many policies will be close to the mean.

Option A is correct.