試題詳解

167. Insurance companies A and B each earn an annual profit that is normally distributed with the same positive mean.The standard deviation of company A’s annual profit is one half of its mean.

In a given year, the probability that company B has a loss (negative profit) is 0.9 times the probability that company A has a loss.

Calculate the ratio of the standard deviation of company B’s annual profit to the standard deviation of company A’s annual profit.
(A) 0.49
(B) 0.90
(C) 0.98
(D) 1.11
(E) 1.71