The average time to run the 5K fun run is 22 minutes and the standard deviation is 2.5 minutes. 45 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 22 b. What is the distribution of ? - N( 22 c. What is the distribution of ? * - N( 990 d. If one randomly selected runner is timed, find the probability that this runner's time will be between 21.9409 and 22.2409 minutes. 0.0478 e. For the 45 runners, find the probability that their average time is between 21.9409 and 2.5 0.3727 16.7705 22.2409 minutes. f. Find the probability that the randomly selected 45 person team will have a total time less than 999. g. For part e) and f), is the assumption of normal necessary? O NoO Yes h. The top 10% of all 45 person team relay races will compete in the championship round. These are the 10% lowest times. What is the longest total time that a relay team can have and still make it to the championship round? minutes

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