Question 447449: A professor gives a 15 question MCQ quiz. For each question in the quiz, there are five choices out of which only one is correct. The professor wants to limit the probability of passing a student who guesses on every question to below 0.05. What is the lowest passing grade (number of questions correctly answered out of 15), the professor can use for the quiz? (*please include workings, thanks!)
(A) 8
(B) 6
(C) 7
(D) 5
(E) None of the above
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A professor gives a 15 question MCQ quiz. For each question in the quiz, there are five choices out of which only one is correct. The professor wants to limit the probability of passing a student who guesses on every question to below 0.05. What is the lowest passing grade (number of questions correctly answered out of 15), the professor can use for the quiz? (*please include workings, thanks!)
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Binomial Problem with n = 15 and p = 1/5
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P(x = # correct) = (15Cx)(1/5)^x*(4/5)^(15-x)
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Solve (15Cx)(1/5)^x*(4/5)^(15-x) < 0.05
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Checking your various answers,
I get x = 6
Prob of getting 7 correct is 0.0138 which meets the criteria
but x = 6 also meets the criteria.
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Prob of getting 6 correct is 0.04
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Prob of getting 5 correct is 0.10 which does not meet the criteria.
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Cheers,
Stan H.
(A) 8
(B) 6
(C) 7
(D) 5
(E) None of the above
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