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You are to take a multiple-choice exam consisting of 64 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 exam? (Hint: Your expected score is the mean value of the x distribution.)
32
(b) Compute the variance and standard deviation of x.
Variance = 25
Standard deviation = 5

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amna04352

Answer:

a) 32

b) 16 ; 4

Step-by-step explanation:

a) p(correct) = ½

E(X) = n×p = 64 × ½ = 32

b) p = ½, q = ½

Var = n×p×q = 64 × ½ × ½ = 16

Standard deviation = sqrt(variance)

= sqrt(16) = 4

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