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  3. the average time to run the 5k fun run is 21 minut

The average time to run the 5K fun run is 21 minutes and the standard deviation...

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Statistics

The average time to run the 5K fun run is 21 minutes and thestandard deviation is 2.5 minutes. 13 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 20.2599 and 21.0599minutes.
  5. For the 13 runners, find the probability that their averagetime is between 20.2599 and 21.0599 minutes.
  6. Find the probability that the randomly selected 13 person teamwill have a total time less than 266.5.

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