The average time to run the 5K fun run is 23 minutes and the standard deviation is 2.2 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.
What is the distribution of X? X ~ N(23, 2.2)
What is the distribution of x̄? x̄ ~ N(23, 0.3379)
What is the distribution of Σx? Σx ~ N(989, 67.623)
If one randomly selected runner is timed, find the probability that this runner's time will be between 22.9967 and 23.4967 minutes.
For the 43 runners, find the probability that their average time is between 22.9967 and 23.4967 minutes.
Find the probability that the randomly selected 43 person team will have a total time less than 1001.9.
For part e) and f), is the assumption of normal necessary? YesNo
The top 10% of all 43 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