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

Question

Mathematics

Robbins

3 May, 20:35

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

+3

Answers (1)

Know the Answer?

Damien Bishop · Answer 1

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