A-LevelMathematicsProbability and statistics9709/62 · Feb/Mar 2017 · Q35 Marks

It is found that 10% of the population enjoy watching Historical Drama on television. Use an appropriate approximation to find the probability that, out of 160 people chosen randomly, more than 17 people enjoy watching Historical Drama on television.

(a)Use an appropriate approximation to find the probability that, out of 160 people chosen randomly, more than 17 people enjoy watching Historical Drama on television.[5]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2017). The mark or mark type is shown in brackets.

[B1] Correct unsimplified np and npq (np = 160×0.1 (16), npq = 160×0.1×0.9 (14.4))
[M1] 16.5 or 17.5 seen in standardised eqn for continuity correction
[M1] Standardising need √ (i.e., dividing by standard deviation)
[M1] Correct area from their mean (1 – Φ), final solution
[A1] = 0.346

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Topic: Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source: A-Level Mathematics, Feb/Mar 2017 Paper 6 Variant 2, question 3.

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