Question

The average time to run the 5K fun run is 20 minutes and the standard deviation is 2.3 minutes. 7 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 X X ? X X ~ N(,) What is the distribution of ¯ x x¯ ? ¯ x x¯ ~ 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 19.696 and 20.996 minutes. For the 7 runners, find the probability that their average time is between 19.696 and 20.996 minutes. Find the probability that the randomly selected 7 person team will have a total time more than 137.9. For part e) and f), is the assumption of normal necessary? NoYes The top 10% of all 7 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?

Answer 1