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A-LevelMathematicsProbability and statistics9709/61 · May/June 2020 · Q310 Marks

The masses, in kilograms, of large sacks of flour and small sacks of flour have the independent distributions N(40, 1.5²) and N(12, 0.7²) respectively.

  1. (a)Find the probability that the total mass of 6 randomly chosen large sacks of flour is more than 245 kg.[4]
  2. (b)Find the probability that the mass of a randomly chosen large sack of flour is less than 4 times the mass of a randomly chosen small sack of flour.[6]

Mark scheme

Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.

  1. [M1] N(240, 6 × 1.5²) or N(240, 13.5)
  2. [M1] (245-"240") / √"13.5" (= 1.361)
  3. [M1] 1 – Ф("1.361")
  4. [A1] 0.0867 (3 sf)
  5. [M1] Use of L-4S or similar
  6. [B1] E(L-4S)=-8
  7. [B1] Var(L-4S) = 1.5² + 16 × 0.7² or 10.09
  8. [M1] (0-("-8")) / √"10.09" (=2.519)
  9. [M1] Ф("2.519")
  10. [A1] 0.994 (3 sf)

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About this question

Topic
Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 10 marks.
Source
A-Level Mathematics, May/June 2020 Paper 6 Variant 1, question 3.

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