SOLUTION: The last mid-term examination for math 125 has 100 multiple choice questions. Each question has five possible answers and only one is correct. Many of the students make random gues

Question 384269: The last mid-term examination for math 125 has 100 multiple choice questions. Each question has five possible answers and only one is correct. Many of the students make random guesses for each problem.
i.) Find the mean and standard deviation for the number of correct answers for such student?
ii.) Would it be unusual for a student to pass the exam by guessing and getting at least 60 correct?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The last mid-term examination for math 125 has 100 multiple choice questions. Each question has five possible answers and only one is correct. Many of the students make random guesses for each problem.
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Binomial Problem with n = 100 and p= 1/5
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i.) Find the mean and standard deviation for the number of correct answers for such student?
mean = np = 100*(1/5) = 20
std = sqrt(npq) = sqrt(20(4/5)) = sqrt(16) = 4
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ii.) Would it be unusual for a student to pass the exam by guessing and getting at least 60 correct?
(x >= 60) = 1-binomcdf(100,1/5,59) is near zero to 8 decimal places.
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Cheers,
Stan H.
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