SOLUTION: You are to take a multiple-choice exam consisting of 100 questions with 5 possible responses to each question. Suppose that you have not studied and so must guess (select one of th

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Question 537203: You are to take a multiple-choice exam consisting of 100 questions with 5 possible responses to each question. Suppose that you have not studied and so must guess (select one of the five answers in a completely random fashion) on each question. Let x represent the number of correct responses on the test.
a) what kind of probability does x have?
b) What is your expected score on the exam?
c) Compare the variance and standard deviation of x.
d) based on your answers to parts b and c, is it likely that you would score over 50 on this exam? explain your reasoning behind your answer
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
You are to take a multiple-choice exam consisting of 100 questions with 5 possible responses to each question. Suppose that you have not studied and so must guess (select one of the five answers in a completely random fashion) on each question. Let x represent the number of correct responses on the test.
a) what kind of probability does x have?:::binomial with n = 100 and p = 1/5
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b) What is your expected score on the exam?
expected = np = 100*(1/5) = 20
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c) Compare the variance and standard deviation of x.
std = sqrt(100*1/5*4/5) = 4
var = std^2 = 16
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d) based on your answers to parts b and c, is it likely that you would score over 50 on this exam? explain your reasoning behind your answer
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z(50) = (50-20)/4 = 30/4 = 7 1/2 standard deviations
Since 50 is 7 1/2 standard deviations above the mean
it is highly unlikely a person would score over 50
with no study.
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Cheers,
Stan H.