Ethan has a midterm in his statistics class, which starts 10 minutes after the scheduled end of his biology class. The biology teacher rarely ends class on time though, and the amount of time he is overtime is approximately normally distributed, with a mean of 2 minutes and a standard deviation of 1/2 minute. The time it takes Ethan to get from one class to another is also normal, with a mean of 6 minutes and a standard deviation of 1 minute.
a. Is it reasonable to assume that the two times are independent? Explain.
b. Assuming that the two times are independent, what is the probability that Ethan will be late for his exam?