I have a normal distribution $N$ with $μ=U/2$ and $σ=U/12$ (an approximation of the Irwin-Hall distribution) which has been bounded and normalized to $[0,U]$.
I will now repeatedly generate random numbers $r$ from a uniform distribution with the range $[0,n]$, where $n$ is drawn from $N$.
Is there a name for the distribution formed by the many $r$?
The density of the new distribution seems to be approximated by the complementary cumulative distribution function of the normal normalized by a factor $\frac{10}{\sum\textrm{ccdf}}$.