The cdf of a normal distribution is the error function, or erf(x). The graph looks like this

http://mathworld.wolfram.com/Erf.htmlNow, imagine the graph shifted up by 0.5 (since probabilities are never negative). Basically, a symmetric graph. The mean is in the middle - 0.5

This is a very intuitive graphical way of looking at things, Im sure there is a more "mathematical" solution somewhere.