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jvniki · 2022年12月02日

No.PZ2015120604000178 (选择题)

  1. CFA I
  2. Quantitative

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：

A.

0.5%.

B.

1%.

C.

5%.

解释：

A is correct.

It is appropriate to use the central limit theroy to calculate. Standard error=5.4%/36\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%.

完全没懂题目的意思，怎么看出概率来 呢 标准误和概率的关系是啥了


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星星_品职助教 · 2022年12月02日

同学你好，

这道题求的是the probability that BIM's average capitalization growth rate will over 12.32% in the next three years (all the data are monthly statistics)，关键词是average。

根据这个描述可以看出，要计算的是BIM 's capitalization growth rate的均值大于12.32%的概率。

均值即X bar大于12.32%的概率无法直接得出，但根据中心极限定理可知，X bar服从正态分布，所可以通过正态分布标准化的公式，将P(X＞12.32%)转化成可以查表的标准正态分布，即z分布的形式，进而查表求出概率。

P(X bar＞12.32%)=P(Z＞(12.32%-X bar的均值)/X bar的标准差)

同样根据中心极限定理，X bar的均值=总体均值=10%； X bar的标准差（也就是standard error）=总体标准差/ √n=5.4%/ √6=0.9%，

所以P(X bar＞12.32%)=P(Z＞(12.32%-10%)/0.9%)= P(Z＞2.58)

可以通过标准正态分布表查出2.58对应的左侧概率是0.9951，所以P(Z＞2.58)=0.0049≈0.5%。

也可以通过上课要求背诵的正态分布置信区间关键值，直接得出2.58对应99%的置信区间，所以右侧尾部面积为1%/2=0.5%。

小蜜蜂jj1 · 2023年02月06日

这个n等于6是从哪得来的啊

小蜜蜂jj1 · 2023年02月06日

没事应该是根号36打错了，理解了已经

星星_品职助教 · 2023年03月26日

@SUMMER 已在单独的提问中回复，同样的问题提问一次即可。

星星_品职助教 · 2022年12月08日

@ jvniki average 表明求的是样本的平均值。由于求的是样本均值，所以才服从正态分布，才有之后的步骤。

SUMMER · 2023年03月25日

也可以通过上课要求背诵的正态分布置信区间关键值，直接得出2.58对应99%的置信区间，所以右侧尾部面积为1%/2=0.5%。 老师请问这里为什么要除以2

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