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A-LevelMathematicsProbability and statistics9709/63 · May/June 2025 · Q38 Marks

A machine dispenses coffee into cups. The volume, Vcm³, of coffee in a cup was measured for a random sample of 150 cups. The results were summarised as follows. Σv = 46350 Σv² = 14410800

  1. (a)(i)Calculate unbiased estimates of the population mean, μ, and population variance, σ².[3]
  2. (a)(ii)Calculate a 95% confidence interval for μ.[3]
  3. (b)Without calculation, state whether this confidence interval would be wider or narrower than the confidence interval found in part (a)(ii). Give a reason for your answer.[2]

Mark scheme

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

  1. [B1]
  2. [M1] Use of correct formula.
  3. [A1]
  4. [B1] Seen.
  5. [M1] Any z. Use of correct formula.
  6. [A1] Use of biased (591) gives same interval but scores B1M1A0. Unsupported correct answer scores max B1B1.
  7. [B1] OE.
  8. [B1*] OE.
  9. [B1dep] Dep on previous B1.

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About this question

Topic
Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 8 marks.
Source
A-Level Mathematics, May/June 2025 Paper 6 Variant 3, question 3.

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