Question

A multiple choice test consists of 23 questions with possible answers of a,b,c,d. Estimate the probability that with random guessing the number of correct answers is at least 11.

Answer 1

Binomial Distribution

n = 23

p = 0.25

q = 1 - p = 0.75

P(X 11) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6) + P(X=7) + P(X=8) + P(X=9) + P(X=10)]

So,

P(X 11) = 1 - 0.9851

                  = 0.0149

So,

Answer is:

0.0149