SOLUTION: A multiple-choice quiz has 200 questions, each with 4 possible answers, of which only 1 is the
correct answer. What is the probability that sheer guesswork yields from 25 to 30 co
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Question 1151591: A multiple-choice quiz has 200 questions, each with 4 possible answers, of which only 1 is the
correct answer. What is the probability that sheer guesswork yields from 25 to 30 correct
answers for 80 of 200 problems about which the student has no knowledge?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The probability of a correct answer is 1/4 so E(X) or mean is np or 20 (80*1/4)
variance is np(1-p) or 20*0.75=15.5
sd is sqrt (V)=3.94
guesswork between 25 and 30
normal approximation from 24.5 to 30.5 to include both 25 and 30 (continuity correction factor)
z=(24.5-20)/3.94=1.14
z=(30.5-20)/3.94=2.66
That probability is 0.1232
the exact probability is 0.1194. Without the CCF, the calculated probability would be 0.0981
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