Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet. We randomly sample 49 fly balls. a. If X = average distance in feet for 49 fly balls, then X ~ _______(_______,_______) b. Find the 80th percentile of the distribution of the average of 49 fly balls. Suppose that a category of world-class runners are known to run a marathon (26 miles) in an average of 145 minutes with a standard deviation of 14 minutes. Consider 49 of the races. Let X the average of the 49 races. a. X ~ _____(_____,_____) b. Find the probability that the runner will average between 142 and 146 minutes in these 49 marathons. c. Find the 80th percentile for the average of these 49 marathons. d. Find the median of the average running times. Which of the following is NOT TRUE about the distribution for averages? a. The mean, median, and mode are equal. b. The area under the curve is one. c. The curve never touches the x-axis. d. The curve is skewed to the right