For those interested in reading/studying such, a few observations/ comments:
1. The proof of the CLT should be read First. 2. Generally, these proofs would not be "helpful" for first-time APStat teachers (unless the class has students who have already taken BCCalc And are interested in proofs). 3. One should not assume the second proof (proving the T stat is t-distributed...) is one one can read in an amount of time comparable to the CLT proof: It is time-consuming and requires much focus and time. (It is in a way a careful sampling of an entire math-stat course, and so those who have not seen it before should be ready to spend focused time on such.)
For those who already did get a proof of the CLT, please let me know when requesting the "T Stat Proof" so I don't also attached a CLT proof.
Again, these proofs should not be of concern to first-time APStat teachers, who should be posting questions, especially as authors of the three main textbooks (Dave B, Chris O, and Daren S) are awaiting such questions...
-- David Bee
PS: Of course still make requests for the proof(s) to me off-List. (I should be able to get such to you by no later than the next day.)