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A-LevelMathematicsProbability and statistics9709/62 · Oct/Nov 2025 · Q26 Marks

The random variable X has a normal distribution with mean 10 and standard deviation 3. The independent random variable Y has a Poisson distribution with mean 4.

  1. (a)Find the standard deviation of X + Y.[3]
  2. (b)Find the standard deviation of 5X - Y.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.

  1. [1] (a) Var(Y) = 4
  2. [1] (a) Var(X + Y) = 3² + ‘4’
  3. [1] (a) sd of X + Y = √13 = 3.61
  4. [1] (b) Var(5X) = 5² × 3²
  5. [1] (b) Var(5X - Y) = Var(5X) + Var(Y) = “5² × 3²” + “4”
  6. [1] (b) sd of 5X - Y = √229 or 15.1 (3 sf)

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About this question

Topic
Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source
A-Level Mathematics, Oct/Nov 2025 Paper 6 Variant 2, question 2.

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