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A-LevelMathematicsProbability and statistics9709/61 · Oct/Nov 2022 · Q57 Marks

A builders' merchant sells stones of different sizes.

  1. (a)The masses of size A stones have standard deviation 6 grams. The mean mass of a random sample of 200 size A stones is 45 grams. Find a 95% confidence interval for the population mean mass of size A stones.[3]
  2. (b)The masses of size B stones have standard deviation 11 grams. Using a random sample of size 200, an a% confidence interval for the population mean mass is found to have width 4 grams. Find a.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.

  1. [M1] 45 ± z * 6/√200
  2. [B1] z = 1.96
  3. [A1] 44.2 to 45.8 (3 sf)
  4. [M1] 2 * z * 11/√200 = 4
  5. [A1] z = 2.571
  6. [M1] Φ(their '2.571') = 0.9949 and their '0.9949' – (1 – their '0.9949') [= 0.9898]
  7. [A1] a = 99.0 (3 sf)

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About this question

Topic
Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 7 marks.
Source
A-Level Mathematics, Oct/Nov 2022 Paper 6 Variant 1, question 5.

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