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琳 · 2022年10月20日

不理解

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%.

​知道99%的置信区间对应的是期望加减2.58标准差,但怎么和Z大于2.58对应?两者是如何相等的?

1 个答案

星星_品职助教 · 2022年10月21日

同学你好,

课上要求背诵的关键值中,99%置信区间对应的值为±2.58。这说明在标准正态分布中,当单侧尾部面积为0.5%时,以右尾为例,对应在横轴上的值就是2.58。

具体而言,由于数量中置信区间对应的都是双尾情况,所以99%置信区间相当于双尾总面积为1%,即单尾面积为0.5%。所以,左尾面积为0.5%时,对应在横轴上的值为-2.58;右尾面积为0.5%时,对应在横轴上的值为+2.58.

回到本题,z>2.58,就相当于求+2.58右侧的尾部面积,根据以上的分析,这个面积就是0.5%。

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