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A-LevelMathematicsProbability and statistics9709/61 · Oct/Nov 2019 · Q26 Marks

Annan has designed a new logo for a sportswear company. A survey of a large number of customers found that 42% of customers rated the logo as good.

  1. (i)A random sample of 10 customers is chosen. Find the probability that fewer than 8 of them rate the logo as good.[3]
  2. (ii)On another occasion, a random sample of n customers of the company is chosen. Find the smallest value of n for which the probability that at least one person rates the logo as good is greater than 0.995.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

  1. [M1] Binomial term of form 10Ca pᵃ(1-p)ᵇ 0<p< 1 any p, 0 ≤ a,b ≤ 10
  2. [A1] Correct unsimplified expression
  3. [A1] 0.983
  4. [M1] Equation or inequality involving 0.58ⁿ or 0.42ⁿ and 0.995 or 0.005
  5. [M1] Attempt to solve using logs or Trial and Error. May be implied by their answer (rounded or truncated)
  6. [A1] CAO n=10

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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 2019 Paper 6 Variant 1, question 2.

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