統計謝比雪夫不等式(英文題）

FARIMA

2010-03-12 5:40 am

麻煩請將題目中英文意思，稍微翻成中文(千萬別用翻譯軟體)，列出解題過程
A research study reveals that the mean and standard deviation of the distribution of number of days out of class last year for the students at the begainning of the year are 21 and 6 days, respectively. Please use the Cheyshev inequality to calculate the proportion of the students out of class less than 9 day or more than 33 days is
(A)at least 0.75 (B) at most 0.75 (C) at least 0.25 (D) at most 0.25

回答 (1)

天助

2010-03-12 6:59 am

✔ 最佳答案

研究顯示去年年初學生,沒上學(或不用上學)天數(日數)的平均值與標準差
分別為21天和6天. 請利用Cheyshev不等式求學生沒上學天數小於9天或
大於33天的比例為何?
(A)最少(至少) 0.75 (B)最多(至多)0.75 (C)最少 0.25 (D)最多0.25

By Cheyshev inequality:
x<9 or x>33即 |x-21|>12 or |x-μ|>2σ ,
By Cheyshev inequality
P(|x-μ|>kσ) <= 1/k^2
so, P(|x-μ|>2σ ) <= 1/4=0.25, 即比例(機率)最多 0.25
Ans: (D)

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