Question

On a multiple choice test with 13 questions, each question has four possible answers, one of which is correct. for students who guess at all answers, find the standard deviation for the number of correct answers.

Answer 1

Given:
n = 13, the number of questions
p = 1/4, probability of guessing a correct answer among 4 choices.
q = 3/4, probability of guessing an incorrect answer (q = 1 -p).

The problem is modeled by a binomial distribution.
The mean value is μ = np.
The standard deviation is √(npq).

For the given problem, the standard deviation is
√(13*(1/4)*(3/4)) = 1.561

Answer: 1.56 (nearest hunderdth)