SOLUTION: There are 20 questions in a multiple-choice test. Each question has five choices and one correct answer out of these five choices. A student did not study. He/she answers the qu
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Question 182863: There are 20 questions in a multiple-choice test. Each question has five choices and one correct answer out of these five choices. A student did not study. He/she answers the questions at random. What are the probabilities that he/she makes (i) more than 10-answer right? (ii) exactly eight right?(iii) at most 7 right?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
There are 20 questions in a multiple-choice test. Each question has five choices and one correct answer out of these five choices. A student did not study. He/she answers the questions at random.
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These are binomial problems with n=20, p = 1/2 and q = 1/2
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What are the probabilities that he/she makes
(i) more than 10-answers right?
P(11 < x <= 20) = 1 - P(0<= x <= 10) = 1 - 0.588 = 0.412
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(ii) exactly eight right?
P(x = 8) = 20C8*(1/2)^8*(1/2)^12 = 125970*(1/2)^20 = 0.12
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(iii) at most 7 right?
P(0 <= x <= 7) = 0.132
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Cheers,
Stan H.
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