I'm stuck but here's what I have so far. I'm trying to find the probability that S is bigger than T.
Where do I go from here?
Are S and T independent? I suppose so. Then you should consider the random variable W = S - T and calculate Pr(W > 0).
Originally Posted by Wikipedia at en.wikipedia.org/wiki/Normal_distribution
if X1, X2 are two independent normal random variables, with means μ1, μ2 and standard deviations σ1, σ2, then their linear combination will also be normally distributed: