Question

Step It The ides of insurance is that we all face fisks that are unlikely but carry high cost Think of a fire destroying your home So we form a group to gare the risk: we all pay ?? smal amount, and the insurance polcy pays a large arount to those few of us whose homes burn down. An insurance company locks at the records for millions of homeowners and sees that te mean loss from fire in a year A-$250 per house and that the standard deviation ofthe los s ?-$100 distributien of losses is extremely right-skewed: most people have $0 loss, but &few have lerge losses company plans to sell fire insurance for $250 plus enough to eever its costs and profit Explain clearly why R would be unwise to sel only 12 policies Then explain why selling many thousands of such policies is a safe business The average claim for 12 poices may bo far different from the mean, so the risk of a disastrous laes is high. For thousands of policies the law of large numbers supplies protection against such lose. sening only 12 policies increases the probablity for a total loss, comparing to much smaler probabilty in case of arge number of poices. ? The law of large numbers says that for large num ber af polces, the average clan is equal to the mean ar s250. The efore the risk is much lower when the sands or palicies are sold and not only 12. ? Thede trbution of the mean dalm ls much more Normal he thousands of polides are sold and not only 12. Therefore the company has much more control ver proft and losses when thousands of polidies are sold

Answer 1

Solution: Step 1: Obtain the correct option When the sample size of thousands, the distribution is more Normally distributed than the sample size of 12 Therefore, the correct option is the last option from the beginming Step 2 Obtain the probability Let X be a random variable for the average loss in a year. Thus, the required probability is, 270-250 1000 X-250 P(X>270)-P|741000-)>( 25000 25000 -P(Z >3.1623) 0.00078 0.0008