5. In any given year, bad weather can damage a house. From year to year, the dam

Question

5. In any given year, bad weather can damage a house. From year to year, the damage is random. Let D be the dollar value of damages in any given year, 95% of the time, D = $0 and 5% of the time D $25,000 a. Compute the mean and standard deviation of the damage in any given year Consider 100 houses that are dispersed such that in any given year damages to difference houses are independently distributed random variables. The average damages to these 100 houses is given by D b. What is the expected value of the average damage D. What is the probability that D 2 $2500? c.

Explanation / Answer

a)

from above mean =1250

and std deviation =5448.6237

b) from central limit theorum ; expected value of average damage Dbar =1250

c) here std error of average damage =5448.6237/(100)1/2 =544.8624

hence P(Dbar>=2500)=P(Z>(2500-1250)/544.8624)=P(Z>2.2942)=0.0109

D p(D) DP(D) D2P(D) (D-)2 (D-)2P(D) Boom 0 0.950 0.000 0.000 1562500.000 1484375.000 neutral 25000 0.050 1250.000 31250000.000 564062500.000 28203125.000 total 1 = 1250.00 31250000.000 565625000.000 2= 29687500.0000 std deviation=     =    2 = 5448.6237

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