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A-LevelMathematicsProbability and statistics9709/62 · Feb/Mar 2020 · Q25 Marks

Lengths of a certain species of lizard are known to be normally distributed with standard deviation 3.2 cm. A naturalist measures the lengths of a random sample of 100 lizards of this species and obtains an α% confidence interval for the population mean. He finds that the total width of this interval is 1.25 cm.

  1. Find α.[5]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2020). The mark or mark type is shown in brackets.

  1. [M1] 2z * (3.2 / sqrt(100)) = 1.25; OE Allow without '2 x'
  2. [A1] z = 1.953; SOI
  3. [M1] Φ(‘their 1.953’) (= 0.9746)
  4. [M1] = 1 - 2(1 – 0.9746’); OE
  5. [A1] α = 94.9 or 95; CWO

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About this question

Topic
Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, Feb/Mar 2020 Paper 6 Variant 2, question 2.

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