Although integrating e^(-x^2) dx is a little beyond the scope, even for Calculus BC. But it's still doable. Finding the coefficients of the least squares regression line also requires quite a bit of calculus.
I've always wondered how they treat the theory of continuous pdfs in AP Statistics without calculus. Also, the BC calculus course that I took covered differentiation under the integral sign and some Calc III material after the AP exam was over, which makes evaluating Gaussian integrals almost routine.