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A-LevelMathematicsProbability and statistics9709/61 · Oct/Nov 2024 · Q25 Marks

The masses, in kilograms, of small and large bags of wheat have the independent distributions N(16.0,0.4) and N(51.0,0.9) respectively. Find the probability that the total mass of 3 randomly chosen small bags is greater than the mass of one randomly chosen large bag.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.

  1. [B1] E(S1+S2 + S3 – L) = 16 x 3 – 51 [= -3]
  2. [M1] Var(S1+S2+ S3 - L) = 3 × 0.4 + 0.9 [= 2.1]
  3. [M1] 0-(-3) / √'2.1'
  4. [M1] 1 – Φ('2.070')
  5. [A1] = 0.0192 (3 sf)

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About this question

Topic
Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, Oct/Nov 2024 Paper 6 Variant 1, question 2.

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