A-LevelMathematicsProbability and statistics9709/63 · May/June 2019 · Q58 Marks

On average, 34% of the people who go to a particular theatre are men.

(i)A random sample of 14 people who go to the theatre is chosen. Find the probability that at most 2 people are men.[3]
(ii)Use an approximation to find the probability that, in a random sample of 600 people who go to the theatre, fewer than 190 are men.[5]

Mark scheme

Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.

[M1] Binomial term of form 14Cxp*(1 −p)14-x 0 < p < 1 any p, x ≠ 14,0
[A1] Correct unsimplified answer
[A1] Correct answer
[B1] Correct unsimplified np and npq (or sd = 11.603 or Variance = 3366/25)
[M1] Substituting their µ and σ, (no σ² or √σ) into the Standardisation Formula with a numerical value for '189.5'. Condone ± standardisation formula
[M1] Using continuity correction 189.5 or 190.5 within a Standardisation formula
[M1] Appropriate area Φ from standardisation formula P(z<....) in final solution, (<0.5 if z is –ve, >0.5 if z is +ve)
[A1] Correct final answer

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