Often the first step in determining the probability of an event is determining the probability distribution to which the event belongs. Good statisticians can identify the correct distribution right away; if you learn some simple rules, you can specify the correct distribution just like the experts. In this post, I describe how to identify the three most common continuous distributions: normal, t and chi-square.

Requirements for a normal distribution

Many times you will be told when a distribution is normally distributed. When you are conducting hypotheses tests, you will often assume that the distribution is normal (or at least approximately normal) when the following conditions hold:

- The standard deviation (
*σ*) of the population is known - The sample size (n) is ≥30
- The statistic you are measuring is the sample mean

Requirements for a t distribution

If you are performing a hypothesis test and you are measuring the sample mean, you will need to use a t distribution instead of a normal distribution if either of the following conditions holds:

- The standard deviation (
*σ*) of the population is not known. - The sample size (n) is < 30

Requirements for a chi-square (*Χ*^{2}) distribution

There are numerous situations where a chi-square distribution is indicated. In a first year stats class, you will use chi-square distributions when you are performing a contingency test, a goodness-of-fit test or a test of homogeneity.