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The average time to run the 5K fun run is 22 minutes and the standard deviation...

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Statistics

The average time to run the 5K fun run is 22 minutes and thestandard deviation is 2.5 minutes. 49 runners are randomly selectedto run the 5K fun run. Round all answers to 4 decimal places wherepossible 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 probabilitythat this runner's time will be between 22.0643 and 22.4643minutes.
  5. For the 49 runners, find the probability that their averagetime is between 22.0643 and 22.4643 minutes.
  6. Find the probability that the randomly selected 49 person teamwill have a total time more than 1053.5.
  7. For part e) and f), is the assumption of normal necessary?YesNo
  8. The top 10% of all 49 person team relay races will compete inthe championship round. These are the 10% lowest times. What is thelongest total time that a relay team can have and still make it tothe championship round? minutes

Answer & Explanation Solved by verified expert
3.6 Ratings (319 Votes)
there are more than 4 parts as per policy i am answering first4 partsafor X mean 22    See Answer
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