In any year, the weather can ieflict storm damage to a home. From year to year,

Question

In any year, the weather can ieflict storm damage to a home. From year to year, the damage is random Let Y denote the dollar vakve of damage in any given yea Suppose bat in 95% ofthe years Y-so, but n 5% ofthe years y-st9427 The mean of the damage in any year is 5 971 35 (Round your response to two decimal places) The standard devlation of the damage in any year is S 4234 02 (Round your response to two decimal places) Consider an Trourance poor of 100 people whose homes are sufficiently dspersed so that, in any year, the damage to ifferent homes can be viewed as ndependenty dehibuted random variables Let Y denote the average damage to these 100 homes in a year E(Y) the expected value of the average damage Y is$ 971 35 (Round your response to two decimal places) The probuabilty that Y exceeds 2,00(Round your respose to four decomal places) Erter your answer in the answer box and then click Check Answer All parts showing Cear A 01 ) e 04

Explanation / Answer

z = (given value - mean)/ standard deviation

Thus, z = (2000 - 971.35)/4234.02

z = 0.24

Thus, P(Y bar > 2000)

= P(Z> 0.24) = 1 - 0.5948

= 0.4052

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