The average time to run the 5K fun run is 21 minutes and the standard deviation is 2.6 minutes. 40 runners are randomly selected to run the 5K fun run. Round all answers to 4 decimal places where...

The average time to run the
5K
fun run is
21
minutes and the standard deviation is
2.6
minutes.
40
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
XX ~ N(21,2.6).
What is the distribution of
¯xx¯ ~ N (21, 0.4111).
What is the distribution of
∑x∑x ~ N( 840, 16.4438).
If one randomly selected runner is timed, find the probability that this runner's time will be between 20.8833 and21.4833 minutes. ________ For the40 runners, find the probability that their average time is between 20.8833 and21.4833 minutes. _________ Find the probability that the randomly selected40 person team will have a total time less than 832. _________  For part e) and f), is the assumption of normal necessaryNO.
The top
10% of all40 person team relay races will compete in the championship round. These are the10% lowest times. What is the longest total time that a relay team can have and still make it to the championship round? __________ minutes