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胖婷肥周 · 2022年07月06日

这道题疑问比较多！

  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%.

① 为什么不是除以方差5.4%；而是除以标准误。 我看了有些人提问，老师的回答提到了总体和样本 的关系不能直接除。但是我还是不理解！ ②这个题，如果不是出在这个练习题章节，而是整体的一个考试。我们怎么判断说，原来正态分布中标准化的分母，不能用题干的分母，而是要用一个标准误做分母呢？

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星星_品职助教 · 2022年07月07日

同学你好，

1）总体的标准差显然不能直接当做样本均值的标准差使用。所以需要求出样本均值的标准差，即标准误。5.4%/根号36=0.9%。

2）本题提到了“BIM's average capitalization growth rate”，也就是样本均值，无论任何题型，此时要使用的都是相对应的标准差，也就是标准误。

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