I can find only one kind of distribution where variance is constant as the mean varies; a distribution of random numbers between TOP and BOTTOM. This distribution has mean vary as top-bottom varies, yet s remains constant; s 9-0 = s 109-100; the distribution looks like a rectangle on the x axis with a rippled top, amplitude varies as n.

I'm looking for an example of a Normal distribution where variance is constant as mean varies.

EX 4 year old boys weigh 32 lbs, variance = 4 pounds///8 year old boys weigh 56 pounds, variance = 4 pounds.