Question 115381: This is homework and I have tried I keep coming up with 35 as the answer but different formulas each time......can someone show me the way with this one I am pulling my hair out
I= 50% II= 40% EXACTLY III= 35% = this is what I come up with and I do not think this is right because of the formula...statistics has formulas and this isn't one of them
This is the problem:
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 probability 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.
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Five choices means P(correct answer) = 1/5; P(wrong answer) = 4/5
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The problem is binomial because the student either gets each answer
correct or gets it wrong.
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Let "x" be the number of correct answers.
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He/she answers the questions at random.
What are the probability that he/she makes
(i) more than 10 answer right?
P(x>10) = 1 - binomcdf(20,1/5,10) = 0.00056..
(ii) exactly eight right?
P(x=8) = 20C8(1/5)^8(4/5)^12 = 125970*(2.56*10^-6)(0.068719...)=0.022
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You could also use P(x=8)= binompdf(20,1/5,8) = 0.02216...
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(iii) at most 7 right?
P(0<=x<=7) = binomcdf(20,1/5,7) = 0.9678....
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Comment: The "binompdf" and "binomcdf" are functions on the TI-83
graphing calculator for determining binomial probabilities.
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Cheers,
Stan H.
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