Question

An exam consists of 44 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

Answer:

0.3960

Step-by-step explanation:

X - no of questions answered correct is binomial since each question is independent of the other and there are two outcomes

p = Prob of any one question right = 0.2  (1/5)

n = 44

Normal approximation would be mean = np = 8.8 and Variance = npq = 7.04

Std dev = $\sqrt{7.04} \\=2.65335$

X is N(8.8,2.6534)

Or Z = $\frac{x-8.8}{2.6534}$

Since we approximate discrete to continuous continuity correction is to be applied

$x\geq 10$ means x≥9.5

P(X≥9.5) = 0.3960