At a coal mining facility, a tipple is calibrated to load the weight of = 18.00 tons of coal into each hopper, with a standard deviation of = 0.61 tons. Find the probability that a random sample of 20 hoppers will yield a mean weight between 17.80 tons and 18.20 tons.

4pt a) using probability notation, construct the probability expression being asked for (be sure to include a random variable in your proper probability notation)

3pt b) what assumption is required to actually find the probability in part (a) above?

3pt c) make that necessary assumption in part (b) and find the probability.