Hey alb41192.

For this question be aware that the weighted sum of Normal distributions with means <a,b,c> and variances <x,y,z> where we are finding the linear combination of dX + eY + fZ has a normal distribution ~ N(da + eb + cf,d^2*x + e^2*y + c^2*z).

You can standardize this in terms of Z to get a probability by looking at tables or you can use a computer package like R which is really populat