分布标准化

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，这题目套进正态分布标准化以后，为什么是p（z>2.32%/0.009），就下面这个0.009不应该带入sigma=5.4吗？有点晕

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星星_品职助教 · 2022年11月22日

同学你好，

本题标准化的主体是样本均值，即题干中的“BIM's average capitalization growth rate”。

所以分母上也要是对应的样本均值的标准差，即标准误。标准误（standard error）=总体标准差σ/根号n。在本题中，5.4%为总体标准差，所以标准误为0.054/根号36=0.009.

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分布标准化

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