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 and 21.4833 minutes. ________ For the 40 runners, find the probability that their average time is between 20.8833 and 21.4833 minutes. _________ Find the probability that the randomly selected 40 person team will have a total time less than 832. _________ For part e) and f), is the assumption of normal necessary NO. The top 10% of all 40 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
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
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