Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 253 feet and a standard deviation of 56 feet. We randomly sample 49 fly balls.

a. If X = average distance in feet for 49 fly balls, then X:
b. What is the probability that the 49 balls traveled an average of less than 240 feet? Sketch the graph. Scale the horizontal axis for X. Shade the region corresponding to the probability. Find the probability.
c. Find the 80th percentile of the distribution of the average of 49 fly balls.