这道题为什么用 the central limit theroy 来计算

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%.

为什么用标准误来计算呢，标准误在题干场景里是什么具体含义

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1 个答案

星星_品职助教 · 2023年11月05日

同学你好，

本题中要计算的主体为“BIM's average capitalization growth rate”，这是一个样本的均值（average）。样本均值的标准差就是标准误。

所以在后续对样本均值做标准化时，就需要使用到样本均值的标准差（标准误）。也就涉及到了中心极限定理。

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这道题为什么用 the central limit theroy 来计算

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