Sample average and sample proportion

When the data is interval/ratio, the sample average will be normally distributed when the sample size n is large enough?

When the data is only binary, meaning yes or no, or one way or the other, the sample proportion (number of yes divided by sample size n, or x/n) will be normally distributed when the sample size n is large enough?

How large is large enough for sample average to be approximately Normal?

How large is large enough for sample proportion to be approximately Normal?