Suppose Frederika arrives at bus stop at time, S, uniformly distributed on the interval [ − 5, 5]. Suppose that the bus departs from the bus stop at a time, T, which is normally distributed with mean 0 and standard deviation 4 (S and T are measured in minutes). Suppose S and T are independent. Find the probability that Frederika catches the bus. This is the probability of the event (S < T). Hint: Integrate by parts to do an integral of the form $\int F_T (s)ds$, where F_T is the cumulative distribution of T. Also note that if the bus departs after t=5, then Frederika will catch the bus.
I'm not sure how to get the cumulative distribution of T and then be able to integrate it with respect to s.