試題詳解

168. Claim amounts at an insurance company are independent of one another. In year one, claim amounts are modeled by a normal random variable X with mean 100 and standard deviation 25. In year two, claim amounts are modeled by the random variable Y = 1.04X + 5.

Calculate the probability that a random sample of 25 claim amounts in year two average between 100 and 110.
(A) 0.48
(B) 0.53
(C) 0.54
(D) 0.67
(E) 0.68