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AgnesWu · 2023年12月10日

关于单尾双尾

  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%.

这道题为什么不考虑大于，按照单尾 1% 选择

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2 个答案

品职助教_七七 · 2023年12月11日

嗨，爱思考的PZer你好：


@AgnesWu

能判断单侧还是两侧概率的是P(Z＞2.58)这个表述，其中的大于号，就说明了只需要看2.58这个值右侧的概率。这个概率值求出来就是0.5%。

换而言之，0.5%是在上述前提下求出来的概率面积。不是题干条件，也就不会对单侧还是双侧概率有任何的假定。


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加油吧，让我们一起遇见更好的自己！

品职助教_七七 · 2023年12月10日

嗨，爱思考的PZer你好：


本题做完正态分布标准化后，最后得到的结果是求P(Z＞2.58)。也就是要求2.58这个关键值所对应的右尾概率（面积）是多少。

可直接查表，也可以通过99%置信区间关键值为±2.58，进而来推出2.58所对应的右尾面积是0.5%。

上述每一步都是确定的，不需要选择大于还是小于（只能是大于），也不用选择单尾还是双尾（只能是单尾）。

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

AgnesWu · 2023年12月11日

可直接查表，也可以通过99%置信区间关键值为±2.58，进而来推出2.58所对应的右尾面积是0.5%。——我理解，0.5%就是假定了是双尾的前提

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