Given a bivariate gaussian distribution, I'm attempting to find the probability p for which the ellipse of all points (x,y) for which P(X = x, Y= y) = p contains a given % of the samples drawn from the distribution. I want the 2d equivalent for the 1 dimensional case: given a normal distribution N(0,1): e.g interval between points with p = 0.24197072 contains 68.2% of all samples e.g interval between points with p = 0.05399097 contains 95.4% of all samples e.g interval between points with p = 0.00013383 contains 99.6% of all samples in two dimensions these interval boundries become an ellipse and I'm interested in finding the p value corresponding to a given % (contained samples in contour ellipse with p) value in the 2 dimensional case. Some extra info: A matlab, python (using numpy, scipy?) numerical approximation is ok, I don't need an analytic formula. Actually I just want to draw the ellipses containing 75%, 95%, 99% of the samples in python (using matlibplot) for a given gaussian distribution (varying mean & covariance). I know how to do this if I obtain p first (contour plots). Thank you for reading my question and I hope you can help.