Central Limit Theorem problem I'm struggling with. Any suggestions on how to use a ti-84 plus calculator would be useful too if known. Thank you!

Chapter 7: Central Limit Theorem (Sums) Progresssaved Score: 0/5 0/5 answered ' i The average time to run the 5K fun run is 22 minutes and the standard deviatiOn is 2.5 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. a. What is the distribution of X? X N(:],S) b. What is the distribution of 5:? i - N(S,:]) c. What is the distribution of Z :c? 29: - N(S,:]) d. If one randomly selected runner is timed, find the probability'that this runner's time will be between 22.0282 and 22.3282 minutes. E: e. For the 43 runners, find the probability that their average time is between 22.0282 and 22.3282 | f. Find the probability that the randomly selected 43 person team will have a total time more than 924.5. . For part e) and f), is the assumption of norma! necessary? 0 N00 Yes . The top 10% of all 43 person team relay races witl 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? Eminutes D'UCI Hint: Some Helpful Videos