Suppose Dave and Brian are on the cross country team. After many races, the distribution of his time in the mile run, in minutes, is approximately normal for both Dave and Brian. Suppose (5(3) is the pdf for Dave's times and Min) is the pdf for Brian's times: _ 2 M) 2 J% exp (_ W) , 5(122) = 2;? exp (2[zr 5.5)?) (a) Ifthe coach wants the more consistent runner to run the next race, who should she choose? Why? (b) Ifthe coach wants the person who, on average, runs faster, who should she choose? Why? (c) Who has the higher median time in running the mile? Explain. (d) What is the probability that Brian runs a mile in under 5 minutes? (e) What is the probability that Dave takes more than 8 and a half minutes to run a mile? (f) Assume that the time it takes Brian to run a mile is independent from the time it takes Dave to run a mile. What is the probability that they both run a minute in under 5 and a half minutes