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?

Question

Mathematics

Dakota Wallace

24 May, 00:55

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?

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Answers (1)

Know the Answer?

Aliyah Valentine · Answer 1

0.0160

Step-by-step explanation:

P = 1/5

Q = 4/5

Mean = np

Standard deviation = √npq

P (9
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.