I have physically measured two random variables X and Y and determined their respective mean and standard deviation. Both variables have a gaussian distribution. Now I wish to calculate the probability that a given value of X will be less than a given value of Y.
For example, if variable X has a mean of 100 and a standard deviation of 10 and variable Y has a mean of 120 and a standard deviation of 15, what is the probability of X being less than Y given Y=120?