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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%.

知道99%的置信区间对应的是期望加减2.58标准差，但怎么和Z大于2.58对应？两者是如何相等的？

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星星_品职助教 · 2022年10月21日

同学你好，

课上要求背诵的关键值中，99%置信区间对应的值为±2.58。这说明在标准正态分布中，当单侧尾部面积为0.5%时，以右尾为例，对应在横轴上的值就是2.58。

具体而言，由于数量中置信区间对应的都是双尾情况，所以99%置信区间相当于双尾总面积为1%，即单尾面积为0.5%。所以，左尾面积为0.5%时，对应在横轴上的值为-2.58；右尾面积为0.5%时，对应在横轴上的值为+2.58.

回到本题，z＞2.58，就相当于求+2.58右侧的尾部面积，根据以上的分析，这个面积就是0.5%。

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