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 guess, estimate the probability of getting at least 20% correct.

Answer 1

P(of getting the right answer) = 1/4 = 0.25

Using the normal approximation to the Binomial

Mean = n * p = 60 * 0.25 = 15

Standard Deviation = Sqrt(n * p * (1 - p)) = Sqrt(60 * 0.25 * 0.75) = 3.354

Probability of getting at least 20% means at least 0.2 * 60 = 12

Therefore P(X 12). Using the correction factor for (), we need to find P(X > 12 - 0.5) = P(X > 11.5)

____________________________

P(X > 11.5) = 1 - P(X < 11.5)

Z = (11.5 - 15) / 3.354 = -0.75

The p value for P(X < 11.5) is 0.1492

Therefore the Probability, P(X > 11.5) = 1 - 0.1492 = 0.8508

___________________________________________________________

Continuity Correction Factor Table

1) If P(X = n)        Use P(n – 0.5 < X < n+0.5)

2) If P(X > n)        Use P(X > n + 0.5)

3) If P(X <= n)     Use P(X < n + 0.5)

4) If P(X < n)        Use P(X < n - 0.5)

5) If P(X => n)     Use P(X > n - 0.5)