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A-LevelMathematicsProbability and statistics9709/61 · Oct/Nov 2023 · Q48 Marks

The masses, in kilograms, of chemicals A and B produced per day by a factory are modelled by the independent random variables X and Y respectively, where X ~ N(10.3, 5.76) and Y ~ N(11.4, 9.61). The income generated by the chemicals is $2.50 per kilogram for A and $3.25 per kilogram for B.

  1. (a)Find the mean and variance of the daily income generated by chemical A.[2]
  2. (b)Find the probability that, on a randomly chosen day, the income generated by chemical A is greater than the income generated by chemical B.[6]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.

  1. [B1] Accept 3sf.
  2. [B1]
  3. [B1] Or N(37.1, 102) soi.
  4. [M1] Ft their values for A and B.
  5. [A1] Accept 3sf.
  6. [M1] Standardising with their values from attempt at A income - B income.
  7. [M1] For area consistent with their values.
  8. [A1] cwo

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About this question

Topic
Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 8 marks.
Source
A-Level Mathematics, Oct/Nov 2023 Paper 6 Variant 1, question 4.

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