There are good tables of the frequently used cumulative frequency distributions. These tables have some limitations with respect to the number of percentage points that are available. The main drawback in computer usage of these tables is that large amounts of storage and elaborate search and interpolation techniques are necessary for their use. It is the purpose of this study to present associated numerical methods for digital computer which are satisfactorily accurate and which are reasonably economical in both time and machine memory capacity. To carry out this objective the following procedures were used: 1. A review of literature on numerical approximations-both texts and articles from statistical journals and computer science publications. 2. .Writing test programs in Fortran for all the associated methods which can be obtained. 3. Checking the answers obtained by numerical approximation with the known answers in the table in order to determine usefulness of the numerical method. 4. Writing Fortran subprograms to evaluate those integrals by using the most accurate methods according to the experimental results.