[JDDunn9]

You don't need a monte carlo simulation if you have a known distribution. You can just add the means and variances and solve the equation rather than approximating it with a simulation. Monte carlo is more useful when drawing from an unknown distribution.

[jacques_chester]

My understanding is that while the normal distribution is friendly to simple manipulation, a lot of distributions aren't. Not being a statistician I couldn't tell you why or which.