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Question 31 The average time to run the 5K fun run is 24 minutes and the standard deviation is 2.3 minutes. 47 runners are randomly selected to run the 5K fun run. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of X? X - N( b. What is the distribution of ac? ac - N( c. What is the distribution of a? x - Nd d. If one randomly selected runner is timed, find the probability that this runner's time will be between 23.5967 and 24.0967 minutes. e. For the 47 runners, find the probability that their average time is between 23.5967 and 24.0967 minutes. f. Find the probability that the randomly selected 47 person team will have a total time more than 1146.8. g. For part e) and f), is the assumption of normal necessary? O YesO No h. The top 15% of all 47 person team relay races will compete in the championship round. These are the 15% lowest times. What is the longest total time that a relay team can have and still make it to the championship round? minutes