Question

If one or more claims are filed within the next year with Insurance Company ABC, the sum of the claim amounts follow a normal distribution with a mean of 500 and 4,57 variance of 1200. The probability that a claim will not be filed within the next year 5 with Insurance Company ABC is 0.10. If one or more claims are filed within the next year with Insurance Company XYZ, the sum of the claim amounts follow a normal distribution with a mean of 400 and-u- variance of 1600. The probability that a claim will not be filed within the next year 468 with Insurance Company XYZ is 0.30. Assume that the claims filed with Company ABC and XYZ are independent What is the probability that next year's total claim amount for Company ABC will be greater than Company XYZ's total claim amount? Possible Answers A 0.270 [B (0.287 0.613 D 0.883 0.972

Answer 1

let XNNC 500,1200) -> ABC y ~ N(400,1600) Sexyz P( ABC7х+2) = 0.90 (0.3 + 0-7 (PCX7Y)) pobos Port of - Rob of claine 'no claim claims in ABC in xyz in Xyz PANN (100, 2800) as indep. normal rv. does, for, if Xn N(4,0²) X₂ ~ N(H2, 0722) and X, Xz index = x, X2 ~ N(M, Ilz, 8, ²+0 2 ) X - Y COM

nad pribo 501940.8+ (0:7). PC X=Y70)) = 0.910.3 + 0.7 PC 27.-1001 22 X-4 o se Do oro [ ~ N(100, 2800) = 2 = (x-4) -100 2800 N1011) = 0.9 (0.3 + 0.7. Plzy -1.89)

= (0.8) (0.3 +0.7 C 1-0.02938)) = (019) (0.3 + 016994349 0.883 option ID
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