老师，怎么推出2.58对应的面积是0.5呢

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，怎么推出2.58对应的面积是0.5呢

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星星_品职助教 · 2022年08月22日

同学你好，

上课要求背诵过：正态分布下，99%的置信区间对应关键值为±2.58.

由于 99%置信区间两侧尾部的总面积为1%，可知单侧尾部面积为1%/2=0.5%。

结合上面的关键值，可知+2.58右侧以及-2.58左侧的面积均为0.5%。即P(Z＞2.58)=P(Z＜-2.58)=0.5%。

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老师，怎么推出2.58对应的面积是0.5呢

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