The business of selling insurance is based on probability and the law of large n

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 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 p = $300 and the standard deviation of the loss is sigma = $400. What are the mean and standard deviation of the average loss for 10 policies? (Losses on separate policies are independent. Round your standard deviation to two decimal places.) mu_x = $ _____ sigma_x = $ _____ What are the mean and standard deviation of the average loss for l4 policies? (Round your standard deviation to two decimal Places.) mu_x = $ _____ sigma_x = $ _____

Explanation / Answer

for 10 policies

mean =300

std deviation =std deviation of population/(n)1/2 =126.49

for 14 policies:

mean =300

std deviation =std deviation of population/(n)1/2 =106.90

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