Suppose that a category of world class runners are known to run a marathon (26 miles) in an average of 155 minutes, with a standard deviation of 17 minutes. Consider 49 of the races. Consider the average of the 49 races.

a. In words define the random variable. X=_________

b. Find the probability that the 49 runners have an average time that is less than 150 minutes . Include a complete shaded graph, and write the probability statement.

c. Find the 90th percentile for the average time of the 49 runners . Include a complete shaded graph, and write the probability statement.