Inference on means; the Normal distribution

Abstract

Many natural distributions, including distributions of biological measurements, are approximately symmetric. They have distribution functions looking something like Figure 6.1. The symmetry consists in the upper right-hand section being superposable on the lower left-hand section if the diagram were to be pivoted at the centre point. There is no law that distribution functions must be symmetric. They can be as in Figures 6.2 and 6.3, of the type introduced in Exercise 5.1 and common for heterogeneous populations, like the extreme cases in Exercise 5.2, or more complicated.