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朱明远 · 2021年02月19日

问一道题：NO.PZ2015120604000125

  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%/6\sqrt {\rm{6}}

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

为什么不是1%？


这应该是一个单尾的检验啊，因为题目中要检验的是大于等于12.32%的情况。


大于等于不就是说明这是单尾情况？

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2 个答案

星星_品职助教 · 2021年02月21日

@zzm

回复追问：

这个思路可以解题。原因是假设检验里的test statistics本质就是在做标准化的过程。所以实质仍然是正态分布标准化，这也是这道题目考察的内容。

所以更简单的方法是直接代入标准化的公式就可以了。

星星_品职助教 · 2021年02月20日

同学你好，

这道题目不是一个“检验”。但单尾的理解没问题。这道题标准化后相当于要去求标准正态分布下P(Z＞2.58)的概率。也就是右侧尾部面积。

但注意此时不能直接选择1%。

因为±2.58对应的是标准正态分布下，99%的“置信区间”的关键值。

在数量这个学科中，“置信区间”都处于正态分布的中间位置，左右各会留出一个“尾巴”，这两个尾巴的总面积才是1-99%=1%。单侧尾巴面积是1%/2=0.5%

这道题求的P(Z＞2.58)对应的只是右侧尾巴的面积，也就是0.5%。并不是两个尾巴的面积和1%。

可参考下图进行理解：


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