Track 5 · Probability Distributions · Lesson 10 of 10
Choosing and checking a distribution
Match a situation to a suitable probability model, check the model against data, and judge when the normal approximation to the binomial can be trusted.
An operations analyst wants to staff a contact centre, an actuary wants to price motor insurance, and a race organiser wants to plan finish-line volunteers. Each needs a probability model — and each will make expensive mistakes if the model does not fit the data. Choosing a model is half the job; checking it is the other half.
A distribution is a model: a set of assumptions about how the data were generated. The first step in choosing one is to ask what is being counted or measured. The second is to check that the model's assumptions are plausible — first by thinking, then with the data.
Included with a Formula Quest membership
It has 8 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- Match a situation to the binomial, geometric, hypergeometric, Poisson, exponential, uniform or normal model by what it counts or measures
- Read a normal Q-Q plot to judge normality and the direction of skew
- Use the dispersion index to detect overdispersion in count data
- Apply the normal approximation to the binomial with a continuity correction, and recognise when it fails