Peter and Paul agree to meet at the restaurant at noon. Peter arrives at time normally distributed with mean 12:00 noon, and standard deviation 5 minutes. Paul arrives at a time normally distributed with mean 12:02 P.M., and standard deviation 3 minutes. Assuming the two arrival times are independent, find the chance that (a) Peter arrives before Paul; (b) both men arrive within 3 minutes of noon; (c) the two men arrive within 3 minutes of each other.