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A-LevelMathematicsProbability and statistics9709/63 · May/June 2019 · Q16 Marks

The time taken, in minutes, by a ferry to cross a lake has a normal distribution with mean 85 and standard deviation 6.8.

  1. (i)Find the probability that, on a randomly chosen occasion, the time taken by the ferry to cross the lake is between 79 and 91 minutes.[3]
  2. (ii)Over a long period it is found that 96% of ferry crossings take longer than a certain time t minutes. Find the value of t.[3]

Mark scheme

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

  1. [M1] Using ± standardisation formula for either 79 or 91, no continuity correction
  2. [M1] Correct area (Ф-Ф) with one +ve and one -ve z-value or 2Ф – 1 or 2(Ф-0.5)
  3. [A1] Correct answer
  4. [B1] ±1.751 seen
  5. [M1] An equation using ± standardisation formula with a z-value, condone σ² or √σ
  6. [A1] Correct answer

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About this question

Topic
Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source
A-Level Mathematics, May/June 2019 Paper 6 Variant 3, question 1.

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