Please read section 3.2.4 in Foundations of Agnostic Statistics.
- Pages 108—111
- Section titled The Central Limit Theorem for Sample Means
The authors are pretty excited in their description of the implications of this theorem, saying:
We now present what is often considered the most profound and important theorem in statistics...
Well, they're right! After you read this section, we will come back to lecture about the importance and implications of this result.