为什么不是（12.32-10）/5.4直接标准化呢？

NO.PZ2015120604000178

问题如下：

BIM is a well-developed public company and its market capitalization growth rates over past few decades are normally distributed.The population has a mean of 10% and a standard deviation of 5.4%. An investor wants to figure out the probability that BIM's average capitalization growth rate will over 12.32% in the next three years (all the data are monthly statistics).Which of the following option is most accurate?

选项：

0.5%.

1%.

5%.

解释：

A is correct.

It is appropriate to use the central limit theroy to calculate. Standard error=5.4%/ $\sqrt {\rm{36}}$ P(X＞12.32%)=P(Z＞ (12.32%-10%)/0.009)=P(Z＞2.58). So the corresponding probability is 0.5%.

如题。如果这道题不是出现在章节练习，从哪里判断出来需要用到中心极限定理？

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星星_品职助教 · 2022年03月15日

同学你好，

对一个变量标准化时，要用该变量的均值和标准差。

本题标准化的是样本均值（ BIM's average capitalization growth rate），所以要用该样本均值的标准差，而不能用总体的标准差。

中心极限定理的作用即使判断出此时样本均值的标准差应该为总体标准差 / 根号n。否则求不出来。

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为什么不是（12.32-10）/5.4直接标准化呢？

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