A probability distribution of the claim sizes for an auto insurance policy appea

Question

A probability distribution of the claim sizes for an auto insurance policy appears in the following table. Claims Probability 1 .05 2 .25 3 0.3 4 .25 5 0.15
Find the percentage of claims within one standard deviation of the mean A probability distribution of the claim sizes for an auto insurance policy appears in the following table. Claims Probability 1 .05 2 .25 3 0.3 4 .25 5 0.15
Find the percentage of claims within one standard deviation of the mean Claims Probability 1 .05 2 .25 3 0.3 4 .25 5 0.15
Find the percentage of claims within one standard deviation of the mean

Explanation / Answer

Ans:

mean=3.2

stdandard deviation=sqrt(1.26)=1.12

So,we have to calculate percentage between (3.2-1.12,3.2+1.12)=(2.08,4.32)=(2,4)

hence,the percentage of claims within one standard deviation of the mean=(0.25+0.3+0.25)*100=80%

claims(n) prob.(p) n*p (n-3.2)^2*p 1 0.05 0.05 0.242 2 0.25 0.5 0.36 3 0.3 0.9 0.012 4 0.25 1 0.16 5 0.15 0.75 0.486 Total 1 3.2 1.26

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