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荣 · 2020年05月26日

问一道题：NO.PZ2015120604000178

  1. CFA I
  2. Quantitative

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.

Standatd error=5.4%/6=0.009

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

课上老师讲过significance level即阿尔法，本身已包含单双尾，就是一个概率的意思，应该选1%呀？？？

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1 个答案

星星_品职助教 · 2020年05月26日

同学你好，

不需要考虑单双尾的是p-value的方法，如果p-value小于α，可以直接拒绝原假设，不用考虑单双尾。p-value对应的是假设检验的考点。

这道题并不涉及假设检验，而是在做正态分布的标准化，标准化后的结果相当于在求P(Z＞2.58)的概率，由于我们背过正态分布的那一组关键值，2.58这个critical value对应的是99%的置信区间，也就是剩下双尾的总面积一共为1%，所以P(Z＞2.58)的概率就是右边的那个“尾巴”，也就是0.5%。

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