Choosing Distributions (CIE A Level Maths: Probability & Statistics 2)

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Choosing Distributions

When should I use a Poisson distribution?

  • A random variable that follows a Poisson distribution is a discrete random variable
  • A Poisson distribution is used when the random variable counts something
    • The number of occurrences of an event in a given interval of time or space
  • There are three conditions that must fulfil to follow a Poisson distribution
    • The mean number of occurrences is known and finite (λ)
    • The events occur at random
    • The events occur singly and independently

When should I use a normal distribution?

  • A random variable that follows a normal distribution is a continuous random variable
  • A normal distribution is used when the random variable measures something and the distribution is:
    • Symmetrical
    • Bell-shaped
  • A normal distribution can be used to model real-life data provided the histogram for this data is roughly symmetrical and bell-shaped
    • If the variable is normally distributed then as more data is collected the outline of the histogram should get smoother and resemble a normal distribution curve


Will I still be expected to use the binomial and geometric distribution

  • Knowledge of using the binomial and geometric distribution is expected for Statistics 2
  • Remember the three conditions for both distributions
    • The trials are independent
    • There are exactly two outcomes of each trial (success or failure)
    • The probability of success(p)  is constant
  • You will be expected to recognise when a random variable follows a binomial or geometric distribution and use their properties
    • A binomial distribution will have a fixed finite number of trials(n)
    • A geometric distribution will continue the trials until the first success

Exam Tip

  • Always state what your variables and parameters represent.  Make sure you know the conditions for when each distribution is (or is not) a suitable model.

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Author: Amber

Amber gained a first class degree in Mathematics & Meteorology from the University of Reading before training to become a teacher. She is passionate about teaching, having spent 8 years teaching GCSE and A Level Mathematics both in the UK and internationally. Amber loves creating bright and informative resources to help students reach their potential.