题目
The distribution of one-year returns for a portfolio of securities is normally distributed with an expected value of €45 million, and a standard deviation of €16 million. What is the probability that the value of the portfolio, one year hence, will be between €39 million and €43 million?
选项
A.8.6%
B.9.6%
C.10.6%
D.11.6%
答案
B
解析
We can compute how many standard deviations away from the mean each value would be and refer to the cumulative distribution tables to determine what portion of the probability distribution lies under these points. With a standard deviation of 16 million, the value of 43 million would be: (43-45)/16 or -0.125 standard deviations from the mean 45 and the value of 39 million would be: (39 - 45)/16 or-0.375 standard deviations from the mean. z(-0.125)=0.4522,z(-0.375)=0.3557 0.4522-0.3557=0.0965=9.65% 我们可以计算出每个值与平均值之间有多少标准偏差，并参考累积分布表来确定概率分布的哪些部分位于这些点之下。如果标准差为1600万，则4300万的值将为： （43-45）/ 16或-0.125与均值45的标准差， 而3900万的值将为：（39-45）/ 16或- 与平均值的0.375标准偏差。 z（-0.125）= 0.4522，z（-0.375）= 0.3557 0.4522-0.3557 = 0.0965 = 9.65％