Do the width and /or height of a normal distribution change when its standard deviation remains the same but its means decreases?

Question

Michael · Answer

Well,

what do you mean by "width" ? the domain is (-oo, +oo) ...   ;-)

==> the answer is NO : the shape of the normal curve remains unchanged after a shift of mean

wanna know why ?
because the function is (for a N(µ , σ) meaning : mean = µ, std dev. = σ )

f(x) = (1/ (σsqrt(2pi) ) * e^( - (x - µ)^2/ (2σ^2) )
and what do we see ? 
==> the function is a function of (x - µ)

hope it' ll help !!

Brown eyes · Answer

Thanks for your answer. I found the answer, the answer is it remains the same

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