The average time to run the 5K fun run is 22 minutes and the standard deviation is 2.2 minutes. 41 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-NO
b. What is the distribution of ? -NO
c. What is the distribution of Στο Σα - Ν
d. If one randomly selected runner is timed, find the probability that this runner's time will be
between 21.8846 and 22.1846 minutes.
e. For the 41 runners, find the probability that their average time is between 21.8846 and
22.1846 minutes
f. Find the probability that the randomly selected 41 person team will have a total time less than
906.1.
g. For part e) and f), is the assumption of normal necessary? No Yes
h. The top 15% of all 41 person team relay races will compete in the championship round. These
are the 15% lowest times. What is the longest total time that a relay team can have and still
make it to the championship round?
minutes