[問題] 95 年北科大商管所統計
向各位版大詢問商管所的考古題
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 :
基於單選選擇題，就算是猜題做答應該也是不影響其相互獨立性
我想 80 題中的猜對題數 X~binomial(80,1/4)
P(25 <= X <= 30) 列式
或以 E(X)=20, V(X)=20*1/4*3/4 做常態近似解皆可
但補習班的解法中 Variance 部份卻加入了校正常數項
V(X)=(200-80)/(200-1) * 80*1/4*3/4
在此問題中 "選題" 的動作雖是隨機，但會影響 X 的 Variance 嗎?
純粹是解答有誤?還是我英文會錯意了?
向各位版大請益，感謝不盡。
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01/28 05:34, , 1F
01/28 05:34, 1F