Central limit theorem (sum)

The average time to run the 5K fun run is 23 minutes and the standard deviation is 2.7 minutes. 15 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( b. What is the distribution of ? X - N( c. What is the distribution of > ac? x - NC d. If one randomly selected runner is timed, find the probability that this runner's time will be between 22.0543 and 22.9543 minutes. e. For the 15 runners, find the probability that their average time is between 22.0543 and 22.9543 minutes. f. Find the probability that the randomly selected 15 person team will have a total time more than 349.5. g. For part e) and f), is the assumption of normal necessary? No Yes h. The top 20%% of all 15 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