开发者:上海品职教育科技有限公司 隐私政策详情

应用版本:4.2.11(IOS)｜3.2.5(安卓)APP下载

返回

🎀马小玛🎀 · 2020年05月26日

问一道题：NO.PZ2015120604000178

  1. CFA I
  2. Quantitative

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.

Standatd error=5.4%/6=0.009

P(X＞12.32%)=P(Z＞ (12.32%-10%)/0.009)=P(Z＞2.58). So the corresponding probability is 0.5%.

请问这个题为啥用正太分布标准化做？是从哪里看出要用标准化？

添加评论
2 个答案

星星_品职助教 · 2020年10月17日

@Michelle戀

同学你好，以上解题的逻辑是没问题的。以上答案已经写了这个逻辑：“用背的2.58对应99%置信区间的规律可以得出概率为0.5%”。

与答案不同的原因是：2.58是99%置信区间所对应的关键值。也就是说这个1%是置信区间以外，剩下的两边两个尾巴的总面积为1%，所以根据对称性就可以得出，单尾面积是0.5%。

而本题求的是Z＞2.58的面积，也就是要求右尾的单边面积，所以不是1%，而是0.5%。

星星_品职助教 · 2020年05月27日

同学你好， 思路如下：

题干要求是BIM的 average capitalization growth rate超过12.32%的概率，这里的关键词是“average”，说明要求的是是 X bar＞12.32%的概率。

 然后这道题满足中心极限定理的条件 1. 总体方差已知 2. N＞30 （因为是月度数据取值，所以sample size N=3*12=36）。所以可以得到X bar是服从正态分布的，且X bar作为一个随机变量，他的均值就为总体均值10%，X bar的标准差 (标准误) 即为已知的总体标准差除以根号N，也就是答案解析中的0.009。

所以这道题本质就是在求一个服从正态分布的随机变量大于一个特定的数字的概率，即求P(X bar＞12.32%）。正态分布标准化计算就可以解决这个问题，代入公式标准化后相当于Z＞2.58，查表或者用背的2.58对应99%置信区间的规律都可以得出概率为0.5%

Michelle戀 · 2020年10月17日

你好，请问如何这道题是否可以这么理解： 求备择假设成立的概率，也就是X bar>12.32%, test statistic计算完约为2.58. 2.58为1% level of significance的边界值，结果为1%却与答案不同？请解释下

  • 2

    回答

  • 3

    关注

  • 492

    浏览
相关问题

NO.PZ2015120604000178 问题如下 BIM is a well-velopepublic company anits market capitalization growth rates over past few cas are normally stributeThe population ha meof 10% ana stanrviation of 5.4%. investor wants to figure out the probability thBIM's average capitalization growth rate will over 12.32% in the next three years (all the ta are monthly statistics).Whiof the following option is most accurate? A.0.5%. B.1%. C.5%. A is correct. It is appropriate to use the centrlimit theroy to calculate.Stanrerror=5.4%/36\sqrt {\rm{36}}36​P(X＞12.32%)=P(Z＞ (12.32%-10%)/0.009)=P(Z＞2.58). So the corresponng probability is 0.5%. 本题是求增长率大于12.3%的概率，为什么会用标准误来表示概率？

2024-01-10 13:53 1 · 回答

NO.PZ2015120604000178问题如下BIM is a well-velopepublic company anits market capitalization growth rates over past few cas are normally stributeThe population ha meof 10% ana stanrviation of 5.4%. investor wants to figure out the probability thBIM's average capitalization growth rate will over 12.32% in the next three years (all the ta are monthly statistics).Whiof the following option is most accurate?A.0.5%.B.1%.C.5%. A is correct. It is appropriate to use the centrlimit theroy to calculate.Stanrerror=5.4%/36\sqrt {\rm{36}}36​P(X＞12.32%)=P(Z＞ (12.32%-10%)/0.009)=P(Z＞2.58). So the corresponng probability is 0.5%. 看不懂这道题的提干意思以及求解的顺序和逻辑，请老师解答的详细一些，谢谢

2024-01-03 19:21 1 · 回答

NO.PZ2015120604000178问题如下BIM is a well-velopepublic company anits market capitalization growth rates over past few cas are normally stributeThe population ha meof 10% ana stanrviation of 5.4%. investor wants to figure out the probability thBIM's average capitalization growth rate will over 12.32% in the next three years (all the ta are monthly statistics).Whiof the following option is most accurate?A.0.5%.B.1%.C.5%. A is correct. It is appropriate to use the centrlimit theroy to calculate.Stanrerror=5.4%/36\sqrt {\rm{36}}36​P(X＞12.32%)=P(Z＞ (12.32%-10%)/0.009)=P(Z＞2.58). So the corresponng probability is 0.5%. 这道题为什么不考虑大于，按照单尾 1% 选择

2023-12-10 16:05 2 · 回答

NO.PZ2015120604000178 问题如下 BIM is a well-velopepublic company anits market capitalization growth rates over past few cas are normally stributeThe population ha meof 10% ana stanrviation of 5.4%. investor wants to figure out the probability thBIM's average capitalization growth rate will over 12.32% in the next three years (all the ta are monthly statistics).Whiof the following option is most accurate? A.0.5%. B.1%. C.5%. A is correct. It is appropriate to use the centrlimit theroy to calculate.Stanrerror=5.4%/36\sqrt {\rm{36}}36​P(X＞12.32%)=P(Z＞ (12.32%-10%)/0.009)=P(Z＞2.58). So the corresponng probability is 0.5%. 为什么用标准误来计算呢， 标准误在题干场景里是什么具体含义

2023-11-05 14:07 1 · 回答

NO.PZ2015120604000178问题如下BIM is a well-velopepublic company anits market capitalization growth rates over past few cas are normally stributeThe population ha meof 10% ana stanrviation of 5.4%. investor wants to figure out the probability thBIM's average capitalization growth rate will over 12.32% in the next three years (all the ta are monthly statistics).Whiof the following option is most accurate?A.0.5%.B.1%.C.5%. A is correct. It is appropriate to use the centrlimit theroy to calculate.Stanrerror=5.4%/36\sqrt {\rm{36}}36​P(X＞12.32%)=P(Z＞ (12.32%-10%)/0.009)=P(Z＞2.58). So the corresponng probability is 0.5%. 请问到哪里找这个查表

2023-09-24 10:45 1 · 回答