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Cambridge AS & A Level Mathematics

5.5The normal distribution

The normal distribution in Cambridge AS & A Level Mathematics: what the syllabus expects you to know, the learning objectives and how to practise.
Topic51 practice questions3 lessons
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Learning objectives

What the syllabus expects you to be able to do.

  1. 5.5.1Use a normal distribution to model a continuous random variable and use normal tables.
  2. 5.5.2Find probabilities such as P(X > x₁) given x₁, μ and σ.
  3. 5.5.3Find a relationship between x₁, μ and σ from a given probability.
  4. 5.5.4Recall the conditions for the normal approximation to the binomial and use it with a continuity correction.

Lessons

  • The normal approximation to the binomial distribution

    40 min

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  • The normal distribution: finding values, the mean and the standard deviation

    40 min

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  • The normal distribution: standardising and finding probabilities

    40 min

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Sample question

A sample question on this topic. Answer it, check it, then read the worked answer.

The normal distribution: sample question

1 mark

X∼B(60,0.5)X \sim \mathrm{B}(60, 0.5) is approximated by Y∼N(30,15)Y \sim \mathrm{N}(30, 15). Which probability should be calculated for P(X<18)\mathrm{P}(X < 18)?

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