Normal Distribution: Proving X Follows фX(x)=ф[(x-m)/σ]

[Kinetica]

Show that if X is a normally distributed random variable with parameters mu and σ², then then show that for each real number x we have:

ф_X(x)=ф[(x-m)/σ]
I have really hard time. Any possible hint is greatly appreciated.

 

[micromass]

What is the definition of ф[(x-m)/σ], write out the left hand side and the right hand side.

 

[Kinetica]

I know that

Z= [X-μ]/σ or X=σ Z+μ

I also know that

f(x,μ,σ²)=1/ √(2π^σ) e ^{-(x-μ)2/(2σ2)}=1/σ ф((x-μ)/σ)