老师，第2步的标准化中，分子减均值时为什么要用总体的均值10%？

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%.

是因为sample均值的期待E（x）=趋近于总体均值这个原理吗？但这里并没有说样本的均值是正态分布的，只说了population是正态分布的，怎么得出这一结论呢？

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已采纳答案

袁园_品职助教 · 2022年06月08日

嗨，从没放弃的小努力你好：

通过题干可以看出，这道题满足中心极限定理的条件 1. 总体方差已知是finite variance 2. N＞30 （因为是月度数据取值，所以sample size N=3*12=36）。所以可以得到X bar服从正态分布，且X bar的均值就为总体均值10%，X bar的标准差 (标准误) 即为已知的总体标准差除以根号N，也就是答案解析中的0.009。

注意中心极限定理是推导出均值是正态分布，而且也不要求总体的分布形态。

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老师，第2步的标准化中，分子减均值时为什么要用总体的均值10%？

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