The problem of approximating the exact cumulative binomial probabilities has received a great deal of attention in the literature. Several methods of approximation were suggested. Most of these methods fall in one of two broad classes: the class of normal approximations or the class of Poison approximations. The main goal of this paper is giving a new method which helps the researcher to determine the class he may use. Extensive computer runs show that this method dominates what are known as rules of thumb for the domain of applicability of the normal approximation.