The average time to run the 5K fun run is 24 minutes and the standard deviation is 2.6 minutes. 8 runners are randomly selected to run the 5K fun run. Round all answers to 4 decimal places where...

Extracted text: The average time to run the 5K fun run is 24 minutes and the standard deviation is 2.6 minutes. 8 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( 24 2.6 b. What is the distribution of ? - N( 24 0.9192 v c. What is the distribution of ) x? ) x - N( 192 7.3539 v) o d. If one randomly selected runner is timed, find the probability that this runner's time will be between 23.7212 and 24.9212 minutes. 0.1811 e. For the 8 runners, find the probability that their average time is between 23.7212 and 24.9212 minutes. 0.4611 f. Find the probability that the randomly selected 8 person team will have a total time less than 186.4. 0.2232 g. For part e) and f), is the assumption of normal necessary? O NoO Yes h. The top 15% of all 8 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