A sequence is symmetrically distributed around its arithmetic mean m, and the nu

游客2024-01-13 62

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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