P(Z＞2.58). So the corresponding probability is 0.5%.

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，请问P(Z＞2.58)的概率不是应该是1 - 99% = 1% 吗？为什么要除以2等于0.5呢？

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星星_品职助教 · 2023年03月26日

同学你好，

±2.58是上课背诵的正态分布下99%置信区间的关键值。

数量科目中，置信区间都位于分布的中间，即两边各有一个尾部。这两个尾部的面积总和为1-99%=1%，每个尾部的面积都为1%/2=0.5%。

上述内容用概率来描述，就是右尾P(Z＞2.58)和左尾P(Z＜-2.58)的面积之和为1%，各自的面积都为0.5%。

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P(Z＞2.58). So the corresponding probability is 0.5%.

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