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A-LevelMathematicsProbability and statistics9709/53 · May/June 2020 · Q35 Marks

In a certain town, the time, X hours, for which people watch television in a week has a normal distribution with mean 15.8 hours and standard deviation 4.2 hours.

  1. (a)Find the probability that a randomly chosen person from this town watches television for less than 21 hours in a week.[2]
  2. (b)Find the value of k such that P(X < k) = 0.75.[3]

Mark scheme

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

  1. [M1] P(X<21)=P(z < (21-15.8)/4.2) = Φ(1.238)
  2. [A1] 0.892
  3. [B1] z = ±0.674
  4. [M1] (k-15.8)/4.2 = 0.674
  5. [A1] 18.6

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About this question

Topic
Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, May/June 2020 Paper 5 Variant 3, question 3.

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