Question

The business of selling insurance is based on probability and the law of large numbers. Consumers buy insurance because we all face risks that are unlikely but carry high cost. Think of a fire destroying your home. So we form a group to share 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. The insurance company sells many policies, so it can rely on the law of large numbers.

In fact, the insurance company sees that in the entire population of homeowners, the mean loss from fire is μ = $300 and the standard deviation of the loss is σ = $400.What are the mean and standard deviation of the average loss for 8 policies? (Losses on separate policies are independent. Round your standard deviation to two decimal places.)

μX =	$
σX =	$

What are the mean and standard deviation of the average loss for 15 policies? (Round your standard deviation to two decimal places.)

μX =	$
σX =	$

Answer 1

The insurance company sees that in the entire population of homeowners, the mean loss from fire is μ = $300 and the standard deviation of the loss is σ = $400.

To find, mean and standard deviation of the average loss for 8 policies. That is n = 8

We know mean and standard deviation in sampling distribution is,

Therefore, for n=8

	$300
	$141.42

For n=15

	$300
	$103.28