问一道题：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.

$Standatd error = \frac{5.4 %/ \sqrt}{\sqrt{6}} = 0.009$

P(X＞12.32%)=P(Z＞ (12.32%-10%)/0.009)=P(Z＞2.58). So the corresponding probability is 0.5%.

请问能解释一下为何用中心极限定理吗？

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星星_品职助教 · 2020年11月26日

同学你好，

因为通过中心极限定理才能使用总体均值作为X bar分布的均值，总体标准差除以根号n作为X bar分布的标准差（标准误）。但是这其实是一个原理和背景，从本题实际计算的角度出发用不到这些。

建议这道题直接就用正态分布标准化的公式来解就可以了。

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问一道题：NO.PZ2015120604000178

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