Suppose that a category of world class runners are known to run a marathon (26 miles) in an average of 144 minutes with a standard deviation of 11 minutes. Consider 49 of the races.
Let X = the average of the 49 races.
part a. Give the distribution of X. (Round your standard deviation to two decimal places.)
part b. Find the probability that the average of the sample will be between 142 and 147 minutes in these 49 marathons. (Round your answer to four decimal places.)
part c. Find the 70th percentile for the average of these 49 marathons. (Round your answer to two decimal places.)
part d. Find the median of the average running times.
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