# Mean preserving spread for normal distribution

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.

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.