A sequence of n trials from a finite population with no replacement is described by the hypergeometric distribution as the number of successes. Calculating the likelihood that factory-produced items would be defective is one of the most popular uses of the hypergeometric distribution in industrial quality control. Very recently, several researchers have applied this distribution on certain families of analytic functions. In this study, we provide certain adequate criteria for the generalized hypergeometric distribution series to be in two families of analytic functions defined in the open unit disk. Furthermore, we consider an integral operator for the hypergeometric distribution. Some corollaries will be implied from our main results.