  The \textit{Central Limit Theorem (CLT)} is at the heart of a great deal of
applied problem-solving in statistics and data science, but the theorem is
silent on an important implementation issue: \textit{how much data do you need
for the CLT to give accurate answers to practical questions?} Here we examine
several approaches to addressing this issue -- along the way reviewing the
history of this problem over the last 290 years -- and we illustrate the
calculations with case-studies from finite-population sampling and gambling. A
variety of surprises emerge.
