The local field model introduced by Bloembergen, Purcell, and Pound is shown by direct calculation in a specific case to produce a Gaussian local field distribution which shape is often characteristic of nuclear magnetic resonance lines in solids. That this result is obtained is shown to be due to the fact that the binomial distribution describes the local field distribution of a system of spin12particles provided they are more or less uniformly distributed in space and that there is a sufficiently large number of them. In the limit of a large number of spins this distribution is known to become Gaussian in shape so that the local field model can be said to predict a Gaussian line shape under rather general conditions.