Different standard deviations
The formulae on the previous page can be generalised to situations where X1 and X2 have different standard deviations.
The distributions of the sum and difference of two normally distributed variables are now displayed graphically. A simulation supports them.
Heights of husband-and-wife pairs
The video below illustrates these distributions in the context of the heights of a married couple.
The distance between the top of the woman's head and a fixed location (the ground or door frame) has lower spread than the distance to a variable location (the top of the man's head).