The average time to run the 5K fun run is 25 minutes and the standard deviation is 2.4 minutes. 6 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 - N( b. What is the distribution of x? a - N( c. What is the distribution of ) x? ) x ~ N( d. If one randomly selected runner is timed, find the probability that this runner's time will be between 24.9303 and 26.1303 minutes. e. For the 6 runners, find the probability that their average time is between 24.9303 and 26.1303 minutes. f. Find the probability that the randomly selected 6 person team will have a total time less than 141. g. For part e) and f), is the assumption of normal necessary?O Yes h. The top 20% of all 6 person team relay races will compete in the championship round. These are the 20% lowest times. What is the longest total time that a relay team can have and still make it to the No championship round? minutes

Solution: Note: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts. In case you required unanswered sub parts also, kindly re-post those parts separately. Let X be the time to rum the 5K fun run. From the given information, X follows normal distribution with mean µ=25 minutes and a standard deviation σ=2.4 minutes.a. Then, the distribution of X is normal.b. If X follows normal distribution with mean µ and a standard deviation σ, then x-bar follows normal distribution with mean µ and a standard deviation σ/(square root of n). Here, µ=25 The distribution of x-bar is normal. c. Sum of the normal variables is also normal. Then, the distribution summation of X is normal.