Various approximations for distributions are studied, especially those involving the Binomial, Poisson, gamma, and Gaussian (normal) distributions. m-procedures are used to make comparisons. A simple approximation to a continuous random variable is obtained by subdividing an interval which includes the range (the set of possible values) into small enough subintervals that the density is approximately constant over each subinterval. A point in each subinterval is selected and is assigned the probability mass in its subinterval. The combination of the selected points and the corresponding probabilities describes the distribution of an approximating simple random variable. Calculations based on this distribution approximate corresponding calculations on the continuous distribution.