Question

You are to take a multiple-choice exam consisting of 100 questions with 2 possible responses to each question. Let x represent the number of correct responses on the test. A) What is your expected score on the exam?B) Compute the variance and standard deviation of x.

Answer 1

50 ;

25 ;

5

Explanation:

Given that:

Number of multiple choice questions = 100

Number of possible responses = 2

Hence, probability of success, p = 1/2 = 0.5

Using normal approximation :

The expected score = mean = n*p

Expected score (X) = 100 * 0.5 = 50

standard deviation = std(X) = √

Var(X) = n*p*q

q = 1 - p = 1 - 0.5 = 0.5

Variance = Var(X) = (100 * 0.5 * 0.5)

Var(X) = 25

Var(X) = 25

The Standard deviation (Std) = √Var(X)

Std(X) = √25

Std(X) = 5