这个应该怎么算

问题如下：

The recent performance of Prudent Fund, with USD 50 million in assets, has been weak and the institutional sales group is recommending that it be merged with Aggressive Fund, a USD 200 million fund. The returns on Prudent Fund are normally distributed with a mean of 3% and a standard deviation of 7%, and the returns on Aggressive Fund are normally distributed with a mean of 7% and a standard deviation of 15%. Senior management has asked an analyst to estimate the likelihood that returns on the combined portfolio will exceed 26%. Assuming the returns on the two funds are independent, the analyst’s estimate for the probability that the returns on the combined fund will exceed 26% is closest to:

选项：

A.

1%

B.

2.5%

C.

5%

D.

10%

解释：

中文解析：

首先计算均值：

𝜇 = 0.2 ∗ 3% + 0.8 ∗ 7% = 6.2%

然后计算σ：

标准化之后的z值=

因此𝑃(𝑍 > 1.64) = 1 − 0.95 = 0.05 = 5.0%

选C

Since these are independent normally distributed random variables, the combined expected mean return is:

𝜇 = 0.2 ∗ 3% + 0.8 ∗ 7% = 6.2%

Combined volatility is:

The appropriate Z-statistic is:

Therefore, 𝑃(𝑍 > 1.64) = 1 − 0.95 = 0.05 = 5.0%