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

MWW · 2021年06月01日

还是没有看懂为什么k是2。

NO.PZ2017092702000157

问题如下:

For a distribution of 2,000 observations with finite variance, sample mean of 10.0%, and standard deviation of 4.0%, what is the minimum number of observations that will lie within 8.0% around the mean according to Chebyshev's Inequality?

选项:

A.

720

B.

1500

C.

1680

解释:

B is correct. Observations within 8% of the sample mean will cover an interval of 8/4 or two standard deviations. Chebyshev’s Inequality says the proportion of the observations P within k standard deviations of the arithmetic mean is at least 1 - 1/k2 for all k > 1. So, solving for k = 2: P = 1 – ¼ = 75%. Given 2,000 observations, this implies at least 1,500 will lie within 8.0% of the mean.
A is incorrect because 720 shows P = 720/2,000 = 36.0% of the observations. Using P to solve for
k implies 36.0% = 1 – 1/k
2, where k
= 1.25. This result would cover an interval only 4% × 1.25 or 5% around the mean (i.e. less than two standard deviations).
C is incorrect because 1,680 shows P = 1,680/2,000 = 84.0% of the observations. Using P to solve for
k implies 84.0% = 1 – 1/k
2, where k
= 2.50. This result would cover an interval of 4% × 2.5, or 10% around the mean (i.e., more than two standard deviations).

为什么标准差是4%,问在8%的k就成了2?
1 个答案
已采纳答案

星星_品职助教 · 2021年06月01日

同学你好,

题干问均值周围8%的范围(...lie within 8.0% around the mean),由于标准差=4%,所以这个范围即均值周围2倍标准差的范围。

进而代入切比雪夫不等式即可。