Question 756520: The final exam in a math class has 50 multiply choice questions, each with four options and exactly one correct answer. A student needs 60 percent or better on their final in order to receive a passing grade in class. Their alarm clock broke, and they arrive at the exam with just enough time to guess at each of the questions. Find the mean of number of correct answers? Find the standard deviation for the number of correct answers? Would it be unusual for a student to get 60 percent or better? Why or why not?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The final exam in a math class has 50 multiple-choice questions, each with four options and exactly one correct answer.
A student needs 60 percent or better (>= 30 correct) on their final in order to receive a passing grade in class. Their alarm clock broke, and they arrive at the exam with just enough time to guess at each of the questions.
Find the mean of number of correct answers?
P(correct) = 1/4 n = 50
mean = np = 50(1/4) = 12.5
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Find the standard deviation for the number of correct answers?
std = sqrt[npq] = sqrt[12.5*(3/4)] = 3.0619
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Would it be unusual for a student to get 60 percent or better? Why or why not?
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P(x >= 30 correct) = P(30<= x <=50) = 1 - binomcdf(50,1/4,29) = 0.00000016423
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Very unusual.
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Cheers,
Stan H.
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