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A-LevelMathematicsProbability and statistics9709/62 · Feb/Mar 2018 · Q78 Marks

The weights of packets of a certain type of biscuit are normally distributed with mean 400 grams and standard deviation σ grams.

  1. (i)In a random sample of 6000 packets of this type of biscuit, 225 packets weighed more than 410 grams. Find the value of σ.[4]
  2. (ii)In a random sample of 500 packets of this type of biscuit, how many packets would you expect to find with weights that are more than 1.5 standard deviations from the mean?[4]

Mark scheme

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

  1. [M1] Use 1-225/6000 = 0.9625 to find z value
  2. [A1] z value: ± 1.78
  3. [M1] (410-400)/σ = their z (must be a z value)
  4. [A1]
  5. [M1] Attempt at P(Z< -1.5) or P(Z > 1.5)
  6. [M1] Or equivalent expression with values
  7. [A1] Correct to 3sf
  8. [B1ft] 0.1336 used or FT their 4sf probability times 500, (not 0.9625 or 0.0375) rounded or truncated

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About this question

Topic
Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 8 marks.
Source
A-Level Mathematics, Feb/Mar 2018 Paper 6 Variant 2, question 7.

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