?1 points MIntroStat9 4E088. My Notes Ask Your Teacher The business of selling i

Question

?1 points MIntroStat9 4E088. My Notes Ask Your Teacher 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 al 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 ?-S300 and the standard deviation of the loss is ?-$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.) What are the mean and standard deviation of the average loss for 13 policies? (Round your standard deviation to two decimal places.)

Explanation / Answer

Sample mean is equal to the population mean

And sample standard deviation = population standard deviation/ ?n

where n is sample size

Given: Mean loss, u =$300

Standard deviation loss, s = $400

For n = 8

ux= $300

sx = 400/?8 = $141.42

For n = 13

ux = $300

sx = 400/?13 =$110.94

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