Is it true that any two normal distributions with the same mean can be ordered w.r.t. the relation of a mean preserving spread? My intuition would be that this is true but I cannot come up with a formal proof.
Thanks in advance
Hint: If both normal distributions have the same mean $\mu$, there is a positive constant $c$ such that $F_1(x + \mu) = F_2(c x + \mu)$ where $F_1$ and $F_2$ are the CDF's.