A multiple choice test consists of $20$ questions, each with four possible answers, of which only on

Question

A multiple choice test consists of $20$ questions, each with four possible answers, of which only one is correct. If a student randomly chooses the answer to each question, find the probability of getting at least four but less than nine correct answers. [2] Suppose that each correct answer is awarded five marks and each incorrect answer carries a penalty of one mark, what is the expected score obtained by a student? [2] Using a suitable approximation, find the probability that the mean score of $50$ randomly selected students is more than $12$ marks. State an assumption necessary for your answer to be valid. [4]

Accepted Answer

(i) $0.734\text{ (3 s.f.)}$ (ii) $10$ marks (iii) $0.112\text{ (3 s.f.)}$, assuming independent students who guess every answer randomly.

NJC Sampling Tutorial Q4

NJC Sampling Tutorial Q4

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