作者hexjacal (黑麻糬)
看板Statistics
标题[问题] 95 年北科大商管所统计
时间Thu Jan 26 16:37:10 2012
向各位版大询问商管所的考古题
A multiple-choice quiz has 200 questions each with four possible
answers of which only one is the correct answer. What is the probability
that sheer guesswork yields from 25 to 30 correct answers for 80 of the
200 problems about which the student has no knowledge?
小弟想法 :
基於单选选择题，就算是猜题做答应该也是不影响其相互独立性
我想 80 题中的猜对题数 X~binomial(80,1/4)
P(25 <= X <= 30) 列式
或以 E(X)=20, V(X)=20*1/4*3/4 做常态近似解皆可
但补习班的解法中 Variance 部份却加入了校正常数项
V(X)=(200-80)/(200-1) * 80*1/4*3/4
在此问题中 "选题" 的动作虽是随机，但会影响 X 的 Variance 吗?
纯粹是解答有误?还是我英文会错意了?
向各位版大请益，感谢不尽。
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1F：推 panda0822:因为是有限母体 必须要校正 80/200>5% 01/28 05:34