[求助]方差问题还是一点思路都没有

wanlei

Two different groups of test-takers received scores on the GXYZ standardized test.Group A's scores had a normal distribution with a mean of 460 and a standard deviation of 20.Group B's scores had a normal distribution with a mean of 520 and a standard deviation of 40.If each group has the same number of test-takers,what fraction of the test-takers who scored below 440 belonged to Group B?

题目的答案是1/9 

不知道是怎么算出来的  这种题应该怎么做啊？

G0606

Two different groups of test-takers received scores on the GXYZ standardized test.Group A's scores had a normal distribution with a mean of 460 and a standard deviation of 20.Group B's scores had a normal distribution with a mean of 520 and a standard deviation of 40.If each group has the same number of test-takers,what fraction of the test-takers who scored below 440 belonged to Group B?

此题求 低于440的B组成员个数/（低于440的A、B两组成员个数）

首先，正态分布一倍方差概率0.68，两倍方差概率0.954（摘自反舰导弹火力分配的概念）

Group A   460-20=440

 低于440的个数 相当于小于1倍方差的一半，即1个方差的一半：

                                      （1-0.68）/2=0.16

Group B   520-2*40=440

 低于440的个数 相当于小于2倍方差的一半，即2个方差的一半

                                       (1-0.954)/2=0.023

低于440的B组成员个数/（低于440的A、B两组成员个数）

=0.023/（0.023+0.16）=0.023/0.183

大约是1/9

这题有点难，估计不会考

[此贴子已经被作者于2007-5-28 19:40:57编辑过]

wanlei

呵呵 看的还是迷迷糊糊的  谢谢啊  这么搞的题目LS也能做 牛啊

不过最让人振奋的就是最后一句话