random methods

[Gribouillis]

if i use 240 for N then my pseudo bell curve would have bounds that are 240 apart making these random values just right

That's because you don't really understand the central limit theorem. When you sum N random numbers equidistributed in [0, 1], the mean value is N/2 which is 240/2 = 120 sec = 2 minutes in your case, but the standard deviation is sqrt(N/12) which is sqrt(240/12) = 4.5 seconds in your case. It means that you'll find a random waiting time of 22 minutes with a standard deviation of 4.5 seconds, probably not what you want.

With my code, you can choose the standard deviation. Of course, the law is not exactly a Bell curve, it is a Bell curve truncated to the intervall [20, 24], but as @ndc85430 said above, if the standard deviation is not too large, it amounts to approximately the same thing.