SOLUTION: 4. Elizabeth had a bad night and didn’t study for her English test. She is so stressed that she can’t remember anything about Oedipus Rex. Her test is 20 multiple choice questions

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Question 560851: 4. Elizabeth had a bad night and didn’t study for her English test. She is so stressed that she can’t remember anything about Oedipus Rex. Her test is 20 multiple choice questions with 5 possible answers each. She has no choice but to guess on each question.
a. How many questions can Elizabeth expect to get correct by guessing?
b. What is the probability that she passes the test? (Her final grade is at least a 70.)
c. What is the probability that Elizabeth answers only 5 questions correctly?
d. What is the probability that she answers less than 10 questions incorrectly?

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Her test is 20 multiple choice questions with 5 possible answers each. She has no choice but to guess on each question.
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Binomial Problem with n = 20 and p(correct) = 1/5
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a. How many questions can Elizabeth expect to get correct by guessing?
Ans: np = 20*(1/5) = 4
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b. What is the probability that she passes the test? (Her final grade is at least a 70.)
P(14 <= x <= 20)) = 1 - binomcdf(20,0.2,13) = 0.000001845
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c. What is the probability that Elizabeth answers only 5 questions correctly?
P(x = 5) = 20C5(1/5)^5*(4/5)^15 = 0.1746
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d. What is the probability that she answers less than 10 questions incorrectly?
P(0<= x <= 9) = binomcdf(20,0.2,9) = 0.9861
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Cheers,
Stan H.
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