Question 821846: John is taking an exam, but hasn’t studied or gone to class all term. He figures on guessing all the answers and hoping to get lucky. The test contains 100 multiple-choice questions. Each question has 5 possible answers, only one of which is the correct answer.
What are John’s chances of scoring:
a. exactly 70 on the exam?
b. 70 or better on the exam?
c. 90 or better on the exam?
Found 2 solutions by richwmiller, stanbon:
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! Unless the test counts for everything, it doesn't matter what he gets on the test.
There isn't a chance in hell he will get a 70 and hell will freeze over before he gets more than that.
Answer by stanbon(75887)  (Show Source):
You can put this solution on YOUR website! The test contains 100 multiple-choice questions. Each question has 5 possible answers, only one of which is the correct answer.
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Binomial with n = 100 and p(correct) = 1/5
What are John’s chances of scoring:
a. exactly 70 on the exam?
P(x = 70) = 100C70(1/5)^70*(4/5)^30 = binompdf(100,1/5,70) = 4.29x10^-27
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b. 70 or better on the exam?
P(70<= x <=100) = 1 - binomcdf(100,1/5,69) = 0 to 9 decimal places
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c. 90 or better on the exam?
P(90<= x <=100) = 1 - binomcdf(100,1/5,89) = 0 to 9 decimal places
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Cheers,
Stan H.
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