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森迪 · 2024年01月10日

本题是求增长率大于12.3%的概率，为什么会用标准误来表示概率？

  1. CFA I
  2. Quantitative

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：

A.

0.5%.

B.

1%.

C.

5%.

解释：

A is correct.

It is appropriate to use the central limit theroy to calculate. Standard error=5.4%/36\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%.

本题是求增长率大于12.3%的概率，为什么会用标准误来表示概率？

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1 个答案

品职助教_七七 · 2024年01月10日

嗨，爱思考的PZer你好：


本题求的是​P(X＞12.32%)，其中X为BIM's average capitalization growth rate，没有用标准误来表示概率。

标准误仅在将上述X做标准化时，由于标准化公式的分母需要使用到X的标准差，此时才会用到BIM's average capitalization growth rate的标准差，也就是标准误。

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