I saw the following cartoon about probability and statistics the other day:
The joke in the above picture being that "the top 1%" (i.e. the integral of the gaussian probability distribution function that results in an answer greater than 0.99) is not located at the top of the bell curve ("most probable value"), but rather located on the far right side:
However, I read a comment saying that if this bell curve (i.e. gaussian probability distribution function) was in 2 dimensions (i.e. bivariate) instead of 1 dimension (i.e. univariate) : the integral of this bell curve would no longer be an "area", but rather a "volume" - and if you were to integrate a bivariate gaussian probability distribution function, the "top 1%" would be in the region identified in the above cartoon.
My Question: Can someone please tell me if this cartoon would be mathematically correct if it were a bivariate gaussian probability distribution function?