Fifteen male economists are in a life raft with a maximum carrying capacity of 2850 pounds. The distribution of weights x of male economists is normal with a mean of 178 pounds and a standard deviation of 17 pounds.

(a) Find the probability that a randomly chosen economist weighs more than 189 pounds.

(b) Find the probability that a randomly chosen economist weights between 180 and 190 pounds.

(c) Find the lower bound of average weight of the economists beyond which the boat will be overloaded.

(d) Find the probability that the average weight of the 15 economists exceeds the lower bound of average you calculated in part c.