Distributing values across differing number of columns

[Snappleton]

Good afternoon all. New guy here.
There is likely an easy solution but I cannot seem to get my head around it. I have a templated distribution of values to create a certain shaped bell curve. The template uses 12 columns (numbers) that I need to be able to distribute against varying numbers of columns. Ideally I could enter the number of columns and the spreadsheet would populate cells with values based on the template to conclude with a replica distribution but against some other number of columns (More or less).
I hope this makes sense.

 

[p45cal]

I present the attached as an awful solution; there HAS to be a better way! I was playing around with possibles and what I've included is what I first got to (sort of) work. It uses pure school level arithmetic, no mathematics.
See the named lambda formula in cells C16 and C20.

 

[Snappleton]

I think that solves my problem/question. Much appreciated.