The average time to run the 5K fun run is 21 minutes and the standard deviation is 2.7 minutes. 43 runners are randomly selected to run the 5K fun run. Round all answers to 4 decimal places where possible and assume a normal distribution.

1. What is the distribution of XX? XX ~ N(,)
2. What is the distribution of xx? xx ~ N(,)
3. What is the distribution of xx? xx ~ N(,)
4. If one randomly selected runner is timed, find the probability that this runner's time will be between 21.0824 and 21.4824 minutes.
5. For the 43 runners, find the probability that their average time is between 21.0824 and 21.4824 minutes.
6. Find the probability that the randomly selected 43 person team will have a total time less than 877.2.
7. For part e) and f), is the assumption of normal necessary? YesNo
8. The top 20% of all 43 person team relay races will compete in the championship round. These are the 20% lowest times. What is the longest total time that a relay team can have and still make it to the championship round? minutes