Question

The average time to run the 5K fun run is 23 minutes and the standard deviation is 2.4 minutes. 17 runners are randomly selected to run the 5K fun run. Round all answers to 4 decimal places where possible and assume a normal distribution.

1. What is the distribution of XX? XX ~ N(,)
2. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
3. What is the distribution of ∑x∑x? ∑x∑x ~ N(,)
4. If one randomly selected runner is timed, find the probability that this runner's time will be between 22.7268 and 23.2268 minutes.
5. For the 17 runners, find the probability that their average time is between 22.7268 and 23.2268 minutes.
6. Find the probability that the randomly selected 17 person team will have a total time more than 375.7.
7. For part e) and f), is the assumption of normal necessary? YesNo
8. The top 10% of all 17 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

Answer 1

a. The distribution of X is ,

b. The distribution of

Where ,

c. The distribution of is ,

Where ,

d. Now ,

; From standard normal distribution table