Points on a curve, both from a list and random

if I have a list of distances or percentages( if using domain 0…1) is there a way to ask divide curve to place them as points on a line ? Alternatively, can I get random points along a line using divide curve ?
I have tried so many ways of doing this with random but it always seems to end up with a symmetrical group of points about a mid point.
Any advice would be appreciated

I think you can use the Shatter component and feed it a reparametrized curve and a list of random numbers for this

thanks, I will try that

ooo…that looks clean…thanks