Two measurements X and Y are used to measure w, the weight of a new ship. Suppose X follows a normal distribution with mean w and standard deviation 0.006w, Y follows a normal distribution with mean w and standard deviation 0.004w.

(a) (5 points)Suppose that X and Y are independent, what is the probability that their average value is within 0.005w of the weight w?

(b) (5 points) Suppose that X and Y are not independent, and their correlation coefficient is 0.2. What is the probability that their average value is within 0.005w of the weight