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A-LevelMathematicsProbability and statistics9709/61 · May/June 2018 · Q58 Marks

In Pelmerdon 22% of families own a dishwasher.

  1. (i)Find the probability that, of 15 families chosen at random from Pelmerdon, between 4 and 6 inclusive own a dishwasher.[3]
  2. (ii)A random sample of 145 families from Pelmerdon is chosen. Use a suitable approximation to find the probability that more than 26 families own a dishwasher.[5]

Mark scheme

Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.

  1. [M1] One binomial term ¹⁵Cxpˣ(1 –p)¹⁵⁻ˣ 0<p<1
  2. [A1] Correct unsimplified expression
  3. [A1] Correct answer
  4. [B1] Correct unsimplified mean and variance
  5. [M1] Standardising must have sq rt
  6. [M1] 25.5 or 26.5 seen as a cc
  7. [M1] Correct area Φ, must agree with their u
  8. [A1] Correct final answer accept 0.861, or 0.860 from 0.8604 not from 0.8599

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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 2018 Paper 6 Variant 1, question 5.

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