请问2.58对应的一定是0.05吗？

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%.

请问2.58对应的一定是0.05吗？这里双尾（1-99%）/2=0.05，那单尾不是0.1吗？为什么不考虑是单尾？

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星星_品职助教 · 2022年09月03日

同学你好，

2.58对应的是正态分布中，右侧尾部面积为0.5%。

可根据课上要求背诵的关键值来迅速得到这个结论，即2.58是正态分布下99%置信区间所对应的关键值。

在数量科目中，所有的置信区间都对应双尾的情况，即99%置信区间的两侧两个尾巴的总面积为1%。由此可知单侧尾部面积为1%/2=0.5%。

也就是+2.58所对应的右侧尾部面积为0.5%。所以本题中的P(Z＞2.58).可直接选出A选项0.5%。

同理，-2,.58对应的左侧尾部面积也为0.5%。

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请问2.58对应的一定是0.05吗？

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