Question

A multiple choice test consists of 60 questions. Each question has 4 possible answers of which one is correct. If all answers are random guesses, Estimate the probability of getting at least 12 correct answers. (Hint: Use the Normal Approximation to binomial).

Answer 1

0.8508

Explanation:

In this question, we are asked to estimate the probability of getting at least 12 correct answers.

X ~ Bin ( n , p)

Where n = 60 , p = 1/4 = 0.25

Mean = np = 60 * 0.25 = 15

Standard deviation = sqrt [ n p ( 1 - p) ] = Sqrt [ 60 * 0.25 ( 1 - 0.25) ] = 3.3541

Using normal approximation

P(X < x) = P(Z < ( x - mean) / SD )

P(X >= 12) = P(X > 11.5)

= P(Z > ( 11.5 - 15) / 3.3541 )

= P(Z > -1.04)

= P(Z < 1.04)

= 0.8508