Apply a bell curve to a float through $xf (x)$, where $f(x)$ is some kind of bell curve.

Question

I have a float value that can range from 0 through 8x. I want to apply this float value to scale some numbers, but don't want large scaling so I would like to clamp this to within a range. The range for clamping is 0.25 through 2. If I use the input float as it is, all numbers above 2 will be clamped and wont have any visible effect as they are varied. I won't them to have at least some effect, even though it maybe minimal. So I thought of replacing a linear scaling with a bell curve scaling, with the idea that the bell curve will help bring in (compress) the larger numbers. I am hoping that the f (x) = x * ndf (x) will do this for me. Where ndf is the normal distribution, with its mean at 1.0 and some std deviation possibly 0.75? I need to select a std deviation such that after applying this that the function will still be monotonically increasing for increasing x values. This is for increasing values of x, x * bell-curve (x) is monotonically increasing. Can I choose a std deviation value such that f(x) will increase monotonically? Would anyone be able to explain qualitatively what sort of shape a curve that has x * ndf (x) has.