SOLUTION: 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 question

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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