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Katherine · 2023年09月12日

这题

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:

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%.

为什么这题是÷0.009而不是除以标准差呢,我记得有个公式是x-均值除以标准差,符合正态分布0,1

1 个答案

星星_品职助教 · 2023年09月13日

本题要对样本的均值做标准化,所以也要除以的是样本均值的标准差,即根据中心极限定理所计算出来的标准误=σ/ √n 。

标准差σ=5.4%是总体的标准差。


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