Distribute Split % of Total, with Deviation

I'm trying to apportion a value between two buckets / classify N outcomes such that:

• X% are "Low Priority"
• 100% -X % are "High Priority"

I've got a percentage value of X% and a deviation, but I'm struggling with the distribution aspect. Frequently for example, I end up calculating an X that is effectively above 100% when using a normal distribution, a value of X of ~0.95 and a deviation of 0.026. For example, occasionally I'll end up with 102.83% X and thus -2.83% for X', which is clearly not possible in my data.

Logically is a normal distribution the right construct to use here? My other guess was basically to sample up to N times, and for each N randomly select is it low/high based on an absolute scalar value - but this feels like a brutal approach that would perform poorly for large N's?

Questions mainly are:

• Am I on the right track at all?
• Should I be using another distribution here in lieu of the normal, to calculate the split/spread of X vs 1-X total?
• If I'm using an appropriate distribution, how do I correctly handle the wrap-around effect of over-running my range?
• Why are you using a distribution at all? You have some cases, you call (say) 5% of them high-priority — but that does not require a distribution. Nov 24 '21 at 2:17