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A sequence is symmetrically distributed around its arithmetic mean m, and the nu
A sequence is symmetrically distributed around its arithmetic mean m, and the nu
游客
2025-02-23
37
管理
问题
A sequence is symmetrically distributed around its arithmetic mean m, and the numbers that fall in the standard deviation d count for 68% of the total numbers in the sequence. What’s the percentage of numbers that fall below m+d?
选项
A、16%
B、68%
C、50%
D、32%
E、84%
答案
E
解析
此题考查对正态分布密度函数公式的理解。正态分布曲线为钟形,关于x=α(α为均值)对称,在第二部分的知识点中讲过,曲线下面的面积其实代表的是落在某个范围内的概率。
现在m为均值,方差为d,落在方差d内的数占总数的68%,那么在图中就是由d到α+d曲线下面的面积,刚才说过曲线关于x=α对称,那么图中由d到α以及由α到α+d曲线下面的面积都是68%/2=34%。
从均值a到正无穷曲线下面的面积是50%,那么从α+d到正无穷曲线下面的面积是50%-34%=16%,那么落在小于m+d范围内的数的百分比必然是1-16%=84%。
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