You are to take a multiple-choice exem consisting of 100 questions with 2 possib

Question

You are to take a multiple-choice exem consisting of 100 questions with 2 possible responses to each question. Suppose that you have not studied and so must guess (select one of the two answers in a completely random fashion) on each question. Let x represent the number of correct responses on the test.

(a) What is your expected score on the exem? (Hint: Your expected score is the mean value of the x distribution.)


(b) Compute the variance and standard deviation of x.
Variance =  
Standard deviation =

Explanation / Answer

P(correct choice), p = 1/2 = 0.5

n = 100

This is a binomial distribution

a) Expected value = n * p = 100 * 0.5 = 50

b) Variance = n * p * (1 - p) = 100 * 0.5 * (1 - 0.50) = 25

Standard deviation = sqrt(25) = 5

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