Question

An exam consists of 47 multiple-choice questions. Each question has a choice of five answers, only one of which is correct. For each correct answer, a candidate gets 1 mark, and no penalty is applied for getting an incorrect answer. A particular candidate answers each question purely by guess-work. Using Normal approximation to Binomial distribution with continuity correction, what is the estimated probability this student obtains a score greater than or equal to 10?

Answer 1

0.0160

Explanation:

P= 1/5

Q= 4/5

Mean = np

Standard deviation= √npq

P(9<x)

n= 47

Mean= 47 × 1/5 = 9.4

Standard deviation= √9.5 × 4/5)

= 2.75

= P(9.5-9.4)/2.74 < z

= P(0.1/2.74) < z

= P(z < 0.036)

= 0.0160.