The variations in properties of four typical natural soils are shown to be random variations about a mean or linear trend, related to the “normal” or “Gaussian” statistical distribution. Examples are given of soil properties following the normal, log-normal, and bi-normal distributions. Properties studied include Atterberg limits, grading, and, for undisturbed samples, strength and compressibility characteristics.A rational basis for the choice of a design parameter, such as strength or compressibility, is the probability that the parameter could be less than the design value. For any particular probability the design parameter can be determined using the normal distribution.In the case of bearing capacity estimates, an analysis of the conventional factor of safety suggests that a suitable value of probability or “risk” of failure for design is of the order of 10−2 to 10−3 per cent.In the case of settlement estimates, upper and lower bounds to the magnitude and rate of settlement can be associated with a particular probability or risk.