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The average time to run the 5K fun run is 23 minutes and the standard deviation is 2.3 minutes. 45 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? XX ~ N(,) What is the distribution of ¯xx¯? ¯xx¯ ~ N(,) What is the distribution of ∑x∑x? ∑x∑x ~ N(,) If one randomly selected runner is timed, find the probability that this runner’s time will be between 22.8856 and 23.1856 minutes. For the 45 runners, find the probability that their average time is between 22.8856 and 23.1856 minutes. Find the probability that the randomly selected 45 person team will have a total time less than 1012.5. For part e) and f), is the assumption of normal necessary? NoYes The top 15% of all 45 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

The average time to run the 5K fun run is 23 minutes and the standard deviation is 2.3 minutes. 45 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 22.8856 and 23.1856 minutes.
5. For the 45 runners, find the probability that their average time is between 22.8856 and 23.1856 minutes.
6. Find the probability that the randomly selected 45 person team will have a total time less than 1012.5.
7. For part e) and f), is the assumption of normal necessary? NoYes
8. The top 15% of all 45 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

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