Test for proportions explanation

I’m having trouble understanding this reading “Test for proportions” in Lesson 2 of week 4. Can someone explain how this is archived from the central limit theorem for Binomial distribution?
Thanks a lot.

Sorry for taking a long time to reply. The central limit theorem is rather complicated, it’s not my primary area of interest, and I did not have a ready answer at hand.

I still don’t have a good answer, but maybe these links will provide some help.

First, understand that for large sample sizes, the binomial distribution approaches that of the normal distribution.

Then, try these lecture notes:

Toward the bottom of the lecture, the factor sqrt(p*(1-p)/20) is developed.