The average time to run the 5K fun run is 24 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.

1. What is the distribution ofX
2. X
3. ?X
4. X
5. ~ N(,)
6. What is the distribution of
7. x
8. x
9. ?
10. x
11. x
12. ~ N(,)
13. What is the distribution of
14. x
15. x
16. ?
17. x
18. x
19. ~ N(,)
20. If one randomly selected runner is timed, find the probability that this runner's time will be between 23.7409 and 24.2409 minutes.
21. For the 45 runners, find the probability that their average time is between 23.7409 and 24.2409 minutes.
22. Find the probability that the randomly selected 45 person team will have a total time less than 1075.5.
23. For part e) and f), is the assumption of normal necessary?NoYes
24. The top 20% of all 45 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