  In 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.
