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A-LevelMathematicsProbability and statistics9709/63 · May/June 2018 · Q26 Marks

The random variable X has the distribution N(−3, σ²). The probability that a randomly chosen value of X is positive is 0.25.

  1. (i)Find the value of σ.[3]
  2. (ii)Find the probability that, of 8 random values of X, fewer than 2 will be positive.[3]

Mark scheme

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

  1. [3] B1 z value ±0.674
  2. [3] M1 ±Standardising with 0 and equating to a z-value
  3. [3] A1 Correct answer www ie not ignoring a minus sign
  4. [3] M1 Any bin of form °Cx(0.75)* (0.25)8-*any x
  5. [3] M1 Correct unsimplified answer, may be implied by numerical values
  6. [3] A1 Correct answer

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About this question

Topic
Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source
A-Level Mathematics, May/June 2018 Paper 6 Variant 3, question 2.

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