symmetry, cdf of std normal distribution

[woolley]

The original question:
draw a graph to show that \(\displaystyle \Phi(a)=1-\Phi(-a)\).

i know that this is because of symmetry and symmetry also implies third moment is zero. how do i draw a graph to show this?

 

[woolley]

third moment is symmetry right? so does third moment of zero mean that the distribution is perfectly symmetric? do i simply draw a bell curve???

 

[daon]

I'd graph f(a) = Phi(a) + Phi(-a) and show it was constant (1).