这道题可以理解为36个月的重复抽样情景吗？

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%.

老师好，这道题可以理解为36个月的重复抽样情景吗？即在未来36 个月的样本下重复抽样，return在12.32%以上的概率，如果可以的话样本标准差S是不是应该等于（1/35）^0.5*5.4%？

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星星_品职助教 · 2023年04月07日

同学你好，

1）36个月相当于样本数量一共就是36（n=36）。不是在36个样本里面再抽样；

2）n=36应用在标准误的公式 s / 根号n的分母中，不影响分子s。即样本标准差已经是给定的了（本题中的“a standard deviation of 5.4%”），不需要另行计算。

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这道题可以理解为36个月的重复抽样情景吗？

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