The average time to run the 5K fun run is 22 minutes and the standard deviation is 2.7 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.

1. What is the distribution ofX X?X X~ N(,)
2. What is the distribution ofxx?xx~ N(,)
3. What is the distribution ofx x ?xxIf one randomly selected runner is timed, find the probability that this runner's time will be between 22.1962 and 22.5962 minutes
4. For the 45 runners, find the probability that their average time is between 22.1962 and 22.5962 minutes.~ N(,)
5. Find the probability that the randomly selected 45 person team will have a total time less than 976.5.
6. For part e) and f), is the assumption of normal necessary?No or Yes
7. 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