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A-LevelMathematicsProbability and statistics9709/53 · Oct/Nov 2022 · Q25 Marks

In a large college, 32% of the students have blue eyes. A random sample of 80 students is chosen. Use an approximation to find the probability that fewer than 20 of these students have blue eyes.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.

  1. [B1] 25.6 and 17.4[08] seen, allow unsimplified. 4.172... implies correct variance.
  2. [M1] Substituting their 25.6 and 17.408 into standardisation formula (any number for 19.5), not σ², √σ.
  3. [M1] Using continuity correction 19.5 or 20.5 in their standardisation formula.
  4. [M1] Appropriate area Φ, from final process, must be probability. (Expect final ans < 0.5). Note: the correct final answer may imply M1 from use of calculator.
  5. [A1] 0.0718 < p <0.0719

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About this question

Topic
Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, Oct/Nov 2022 Paper 5 Variant 3, question 2.

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