问一道题：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.

$S_{x} = \frac{σ}{\sqrt{n}} = \frac{5.4 %}{\sqrt{36}} = 0.009$

The test statistic= (12.32%-10%)/0.009=2.58. So the corresponding probability is 0.5%.

老师，我已经求出用公式求出2.58这个值了，下一步分布怎么画?

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星星_品职助教 · 2019年11月14日

同学你好，

这道题是个正态分布标准化的问题，标准化后算出来的是分位点，对应的是一个概率，需要查表。

原版书附录有正态分布表，找到左列2.5，右列找到0.08，然后看对应的概率。注意Z分布表是累积概率函数的概念，所以看到的是左尾概率，也就是P(Z＜2.58)=0.995。而这道题求得是大于2.58也就是右尾的概率，所以还需要进行转化。P(Z＞2.58)=1-P(Z＜2.58)

这道题其实不用查也行，因为2.58上课要求背过，相当于单边面积0.5%的分位点，所以Z＞2.58直接就可以得出0.5%。加油~

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NO.PZ2015120604000178 问题如下 BIM is a well-velopepublic company anits market capitalization growth rates over past few cas are normally stributeThe population ha meof 10% ana stanrviation of 5.4%. investor wants to figure out the probability thBIM's average capitalization growth rate will over 12.32% in the next three years (all the ta are monthly statistics).Whiof the following option is most accurate? A.0.5%. B.1%. C.5%. A is correct. It is appropriate to use the centrlimit theroy to calculate.Stanrerror=5.4%/36\sqrt {\rm{36}}36P(X＞12.32%)=P(Z＞ (12.32%-10%)/0.009)=P(Z＞2.58). So the corresponng probability is 0.5%. 本题是求增长率大于12.3%的概率，为什么会用标准误来表示概率？

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问一道题：NO.PZ2015120604000178

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