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sarahjia · 2020年02月26日

问一道题：NO.PZ2018062016000088

  1. CFA I
  2. Quantitative

问题如下：

A stock obeying normal distribution has a mean return of 6% and a standard deviation of 18%. The probability for the stock's return to fall less than 4% is:

选项：

A.

37.91%

B.

45.62%

C.

57.68%

解释：

B is correct. Firstly, standardize the original normal distribution：Z= (x-6%)/18%, so P(x <4%) = P( Z<-0.11).

Notice that N(-0.11) = 1- N(0.11). Based on the given table, N(0.11) = 0.5438, so N(-0.11) = 1-0.5438 = 0.4562 = 45.62%

, 老师您好，我的理解是P（Z<-0.1）即为 P(Z>0.11)，为什么F(-0.11)=1-(F(0.11)呢，等式右边求出来的不就是我画的图上一大片区域的面积了吗(包括了中间的区域），谢谢

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1 个答案

星星_品职助教 · 2020年02月26日

同学你好，

要注意F(X)是累积概率函数的意思，也就是X左侧的所有面积。

所以F(0.11)指的是0.11左侧的所有面积，等式右边：1-(F(0.11)指的就是 0.11这个点右侧的面积，也就是右边尾巴。

由于正态分布的对称性，右尾的面积等于左尾[F(-0.11）]

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NO.PZ2018062016000088问题如下 A stoobeying normstribution ha mereturn of 6% ana stanrviation of 18%. The probability for the stock's return to fall less th4% is:N(0.11) = 0.5438 A.37.91%B.45.62%C.57.68% B is correct. Firstly, stanrze the originnormstributionZ= (x-6%)/18%, so P(x 4%) = P( Z -0.11).NotithN(-0.11) = 1- N(0.11). Baseon the given contion, N(0.11) = 0.5438, so N(-0.11) = 1-0.5438 = 0.4562 = 45.62% 另外题目给的是N也是累积概率的意思吗？为什么给的不是F

2022-10-13 11:19 1 · 回答

NO.PZ2018062016000088问题如下 A stoobeying normstribution ha mereturn of 6% ana stanrviation of 18%. The probability for the stock's return to fall less th4% is:N(0.11) = 0.5438 A.37.91%B.45.62%C.57.68% B is correct. Firstly, stanrze the originnormstributionZ= (x-6%)/18%, so P(x 4%) = P( Z -0.11).NotithN(-0.11) = 1- N(0.11). Baseon the given contion, N(0.11) = 0.5438, so N(-0.11) = 1-0.5438 = 0.4562 = 45.62% 为什么能看出来是FX、有没有可能是T分布、0.11指的就是criticpoint右边区域的面积呢？

2022-09-04 11:03 1 · 回答

NO.PZ2018062016000088 45.62% 57.68% B is correct. Firstly, stanrze the originnormstributionZ= (x-6%)/18%, so P(x <4%) = P( Z<-0.11). NotithN(-0.11) = 1- N(0.11). Baseon the given contion, N(0.11) = 0.5438, so N(-0.11) = 1-0.5438 = 0.4562 = 45.62% 这道题哪句话说的是Z分布，另外x为什么是4呢？不太明白这道题目的意思

2021-11-06 19:42 2 · 回答

45.62% 57.68% B is correct. Firstly, stanrze the originnormstributionZ= (x-6%)/18%, so P(x <4%) = P( Z<-0.11). NotithN(-0.11) = 1- N(0.11). Baseon the given table, N(0.11) = 0.5438, so N(-0.11) = 1-0.5438 = 0.4562 = 45.62%请问考试时如何查表呢？

2021-01-27 22:56 1 · 回答

老师那个0.11是用 （4-6）/18得到的吗？

2020-03-09 23:12 1 · 回答