A sampling distribution is the probability distribution of a given statistic based on a random sample.
When a normal population has the X~N(μ, σ2) probability distribution, the statistic X̄ (sample mean) will have the following sampling distribution.
| Statistic | Sampling distribution |
| X̄ | N(μ, σ2 / n) |
If population 1 and 2 have the probability distributions of X1~N(μ1, σ12) and X2~N(μ2, σ22), respectively, then the statistic X̄1 - X̄2 (difference of two independent sample means) will have the following sampling distribution.
| Statistic | Sampling distribution |
| X̄1 - X̄2 | N(μ1 - μ2, σ12 / n1 + σ22 / n2) |