No.PZ2015120604000178 (选择题)

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：

0.5%.

1%.

5%.

解释：

A is correct.

It is appropriate to use the central limit theroy to calculate. Standard error=5.4%/ $\sqrt {\rm{36}}$ P(X＞12.32%)=P(Z＞ (12.32%-10%)/0.009)=P(Z＞2.58). So the corresponding probability is 0.5%.

这道题没有看懂，为什么这么算？

添加评论

1 个答案

星星_品职助教 · 2023年04月11日

同学你好，

这道题求的是the probability that BIM's average capitalization growth rate will over 12.32% in the next three years (all the data are monthly statistics)，关键词是average。

根据这个描述可以看出，要求的是X的“均值”，即X bar大于12.32%的概率（X为BIM 's capitalization growth rate）。

X bar大于12.32%的概率无法直接得出，但根据中心极限定理可知，X bar服从正态分布，所可以通过正态分布标准化的公式，将P(X＞12.32%)转化成可以查表的标准正态分布，即z分布的形式，进而查表求出概率。

P(X bar＞12.32%)=P(Z＞(12.32%-X bar的均值)/X bar的标准差)

同样根据中心极限定理，X bar的均值=总体均值=10%； X bar的标准差（也就是standard error）=总体标准差/ √n=5.4%/ √6=0.9%，

所以P(X bar＞12.32%)=P(Z＞(12.32%-10%)/0.9%)= P(Z＞2.58)

可以通过标准正态分布表查出2.58对应的左侧概率是0.9951，所以P(Z＞2.58)=0.0049≈0.5%。

也可以通过上课要求背诵的正态分布置信区间关键值，直接得出2.58对应99%的置信区间，所以右侧尾部面积为1%/2=0.5%。

添加评论

1
回答
0
关注
235
浏览

我要回答关注问题

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}}36P(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}}36P(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}}36P(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}}36P(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}}36P(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

No.PZ2015120604000178 (选择题)

1 个答案

1

0

235

相关问题