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A-LevelMathematicsProbability and statistics9709/62 · Feb/Mar 2019 · Q36 Marks

The times taken, in minutes, for trains to travel between Alphaton and Beeton are normally distributed with mean 140 and standard deviation 12.

  1. (i)Find the probability that a randomly chosen train will take less than 132 minutes to travel between Alphaton and Beeton.[3]
  2. (ii)The probability that a randomly chosen train takes more than k minutes to travel between Alphaton and Beeton is 0.675. Find the value of k.[3]

Mark scheme

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

  1. [M1] Using ± standardisation formula, no continuity correction, not σ² or √σ
  2. [M1] Appropriate area Φ from standardisation formula P(z<....) in final solution
  3. [A1] Condone linear interpolation = 0.25243
  4. [B1] ±0.454 seen
  5. [M1] An equation using the standardisation formula with a z-value (not 1 – z), condone σ² or √σ
  6. [A1] B0M1A1 max from -0.45

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About this question

Topic
Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source
A-Level Mathematics, Feb/Mar 2019 Paper 6 Variant 2, question 3.

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