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vee · 2022年11月08日

为什么解答过程要用标准误0.9作为标准差去标准化Z呢？能翻译解释一下吗？

  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%.

为什么解答过程要用标准误0.9作为标准差去标准化Z呢？能翻译解释一下吗？

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1 个答案

星星_品职助教 · 2022年11月08日

同学你好，

标准化公式中的均值和标准差需要相互对应。本题的变量为“BIM's average capitalization growth rate”，这是样本均值的概念，所以对应的标准差也应该是样本均值的标准差，即标准误。

标准误的公式为总体标准差σ/根号n，即5.4% / 根号下36 =0.9%

vee · 2022年11月09日

谢谢

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