Let X denote the time required to do a computation using an algorithm written in Fortran and let Y denote the time required to do the same calculation using an algorithm written in Pascal. Assume that X is normally distributed with mean 10 seconds and standard deviation 3 seconds that Y is normally distributed with mean 9 seconds and standard deviation 4 seconds.
(a) What is the distribution of the random variable X - Y?
(b) Find the probability that a given calculation will run faster using Fortran than when using Pascal.