The diversity factor is an essential tool used for loading of distribution transformers. Typically, diversity factors are approximate values and treated as deterministic. By calculating many sample diversity factors it is possible to develop statistics that describe the diversity factor and use these statistic to perform probabilistic transformer loading. Results from work reported here confirm the independence of the diversity factors calculated by bootstrap sampling of measured residential load data. This paper shows that the diversity factor is not normally distributed as assumed in other work. The Anderson-Darling test shows that the diversity factor obeys a gamma distribution. The statistical nature of the predicted demand with the statistical nature of the transformer loading capability can be merged to arrive at a quantifiable statistical assessment of transformer loading.