Recognise a normal model

X~N(μ,σ²), σ>0, has density exp[-(x-μ)²/(2σ²)]/[σ√(2π)] on all real numbers. It is symmetric about μ, and mean=median=mode=μ. Total area is 1; each side of μ has area 1/2. The inflection points are μ±σ. The standard normal has μ=0 and σ²=1; other normal distributions need not have mean zero.