Probability estimates based on small normal‐distribution samples

Although it is impossible to establish a probability from sample data for a single enterprise so that the ratio of favorable to total future events in the enterprise approaches that probability as the number of events approaches infinity, it is possible to compute the expectation of the probability or expected probability from sample data for a single enterprise so that the ratio of favorable to total future events approaches that quantity as the number of such enterprises approaches infinity. Because of this property of the expected probability, it can serve as a basis for computing the expected return on an investment, with confidence that the actual return will approach the expected return as the number of such investments increases. Computation of expected probability PN based on a random sample from a normal parent population and its applicability to flood-control work are discussed.