5. An insurance company looks at the records for millions of homeowners and conc

Question

5. An insurance company looks at the records for millions of homeowners and conclude the probability of fire in a year is 0.02 for each house and the average loss will be S5,000. Thus the mean loss from fire for each house is $100. Assume the fires are independent. The company plans to sell fire insurance for S150, the mean loss plus $50 to cover its costs and profit. (a) If the company only sells 10 policies, what is the expected profit of the company? (b) Do you think selling only 10 policies is a good idea? Consider the probability of bankruptcy, that is, when the money collected cannot pay for the losses. c) Compute the (approximate) probability of bankruptcy if the company sells 1 million policies.

Explanation / Answer

a) expected profit for the company =10*50 =$500

b)probability of at least one fire =1-P( no fire incident) =1-(1-0.02)10 =0.1829

here even if one fire happens then compamny cannot pays the loss from the premium of (150*10=$1500) ; and because the probability of at least one fire incident is greater then 0.05 level therefore it is not unuusal,

therefore it is not good idea,

c)income from 1 million policies =150*106

threfore least number of accident to go bankrupt =150*106/5000 =150000

expected number of incident =np=106 *0.02 =20000

std deviation =(np(1-p))1/2 =140

here as 150000 is very high number of std deviation from mean value ; therefore it is approximately zero,

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