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).

0.8508

Step-by-step 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