Choose the distribution by identifying what the variable measures and how the data are generated. Use normal for continuous measurements, binomial for the number of successes in a fixed number of trials, and Poisson for the number of events occurring within a fixed interval.
This is part of AHL 4.17, Poisson distribution, which requires you to select an appropriate probability model from context.
| Distribution | Use it when | Required conditions and parameters |
|---|---|---|
| Normal | The variable is continuous and values are distributed approximately symmetrically around a mean, such as heights or measurement errors. | , where is the mean and is the standard deviation. |
| Binomial | You count successes among a fixed number of trials, such as defective items among 40 products. | : fixed , two outcomes per trial, independent trials, and constant success probability . |
| Poisson | You count events in a fixed interval of time, distance, area, or volume, such as calls per hour. | : events occur independently at a constant average rate . |
For example, the mass of a randomly selected apple might be normally distributed because mass is continuous. The number of rotten apples in a box of 20 may be binomial if each apple independently has the same probability of being rotten. The number of customers arriving in ten minutes may be Poisson if arrivals are independent and occur at a constant average rate.
A useful clue for observed count data is that a Poisson variable has
However, this equality alone does not prove that a Poisson model is suitable; the contextual assumptions must also hold.
Common misconception: Poisson is not appropriate for every counting variable. If there is a fixed number of opportunities for success, use binomial; Poisson applies to events occurring across an interval.
In an IB response, state the distribution and justify it using its conditions. Then show the GDC setup, including the correct parameters, before giving the probability to the requested accuracy.