Samping dist phat We all face risks that are rare but carry high costs. Insuranc

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Samping dist phat

We all face risks that are rare but carry high costs. Insurance spreads the risk: everybody pays a small amount, and the insurance company pays a large amount to those few with substantial losses. An insurance company looks at the record for millions of homeowners. The mean loss from fire in a year is mu = $ 240 per person and standard deviation sigma= $ 900. The approximate probability that the loss for a single homeowner will be greater than $ 265 is closest to If the company sells 10000 policies, the approximate probability that the average loss will be greater than $ 265 is closest to If the company sells 100 policies, the approximate probability that the average loss will be greater than $ 265 is closest to

Explanation / Answer

From information given, Xi=265, Xbar=240 and s=sigma/sqrt n=900/sqrt 10000=9. Substitute the value sto obtain the z score.

z=(Xi-Xbar)/s=(265-240)/9=2.78

P(X>265)=P(z>2.65)=0.0040 [Find area beyond z=2.65 in z table]

Xi=265, Xbar=240, s=sigma/sqrt n=900/sqrt 100=90

z=(265-240)/90=0.28

P(X>265)=P(z>0.28)=0.3897

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