4. (4pts) A new runner is preparing to run the Santa Ana River Trail Marathon. It is know that 89% of participants compl

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4 4pts A New Runner Is Preparing To Run The Santa Ana River Trail Marathon It Is Know That 89 Of Participants Compl 1 (111.77 KiB) Viewed 38 times

4. (4pts) A new runner is preparing to run the Santa Ana River Trail Marathon. It is know that 89% of participants complete the marathon within 5 hours of their start time. Previous calculations have shown that the probability of completing a marathon within five hours given that a runner trains a minimum of 350 hours is half of the probability of completing a marathon within five hours given that a runner has less than 350 training hours. If the number of training hours of a marathoner follows a normal distribution with a mean of 300 and a sd of 50, what is the probability that a marathoner can complete the race within the 5 hours given that they train a minimum of 350 hours? Hint: Let D be the event that a marathoner completes the race within 5 hours and T be the event that a runner trained a minimum of 350 hours, then P(D|T) = .5P(D|Tº).