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Question 1 The average time to run the 5K fun run is 20 minutes and the standard deviation is 2.4 minutes. 46 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 a? ~ ~ N( c. What is the distribution of > x? > x - N d. If one randomly selected runner is timed, find the probability that this runner's time will be between 19.8691 and 20.2691 minutes. e. For the 46 runners, find the probability that their average time is between 19.8691 and 20.2691 minutes. f. Find the probability that the randomly selected 46 person team will have a total time less than 910.8. g. For part e) and f), is the assumption of normal necessary? O NoO Yes h. The top 15% of all 46 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