Suppose that a category of world class runners are known to runa marathon (26 miles) in an average of 141 minutes with a standarddeviation of 12 minutes. Consider 49 of the races. Let X = theaverage of the 49 races. Part (a) Give the distribution of X.(Round your standard deviation to two decimal places.) X ~ , Part(b) Find the probability that the runner will average between 138and 142 minutes in these 49 marathons. (Round your answer to fourdecimal places.) Part (c) Find the 80th percentile for the averageof these 49 marathons. (Round your answer to two decimal places.)min Part (d) Find the median of the average running times. min
