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A-LevelMathematicsProbability and statistics9709/62 · Oct/Nov 2024 · Q46 Marks

A population is normally distributed with mean 35 and standard deviation 8.1 . A random sample of size 140 is chosen from this population and the sample mean is denoted by X.

  1. (a)Find P(X> 36).[3]
  2. (b)It is given that P(X < a) = 0.986 . Find the value of a.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.

  1. (36-35) / (8.1÷√140) [= 1.461]
  2. 1 – Ф(‘1.461’)
  3. = 0.0720 (3 sf)
  4. [Φ⁻¹(0.986)] = 2.197 to 2.198
  5. (a-35) / (8.1÷√140) = ± '2.198'
  6. a = 36.5 (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 2024 Paper 6 Variant 2, question 4.

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