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A-LevelMathematicsProbability and statistics9709/63 · May/June 2017 · Q25 Marks

The probability that George goes swimming on any day is 1/3. Use an approximation to calculate the probability that in 270 days George goes swimming at least 100 times.

  1. The probability that George goes swimming on any day is 1/3. Use an approximation to calculate the probability that in 270 days George goes swimming at least 100 times.[5]

Mark scheme

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

  1. [B1] np = 270 × 1/3 = 90, npq = 270 × 1/3 × 2/3 = 60 Correct unsimplified np and npq, SOI
  2. [M1] P(x > 100) = P(z > (99.5-90)/sqrt(60)) = P(z > 1.2264) Standardising using 100 need sq rt
  3. [M1] Continuity correction, 99.5 or 100.5 used
  4. [M1] = 1-0.8899 Correct area 1 – Φ implied by final prob. < 0.5
  5. [A1] = 0.110

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About this question

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

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