2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/130968In this paper, we derive a necessary and sufficient condition on the parameters of the Hypergeometric distribution for weak convergence to a Normal limit. We establish a Berry-Esseen theorem for the Hypergeometric distribution solely under this necessary and sufficient condition. We further derive a nonuniform Berry-Esseen bound where the tails of the difference between the Hypergeometric and the Normal distribution functions are shown to decay at a sub-Gaussian rate.ProbabilityStatistics TheoryPrimary 60F05; Secondary 62E20text