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In: Statistics and Probability

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

The average time to run the 5K fun run is 21 minutes and the standard deviation is 2.5 minutes. 13 runners are randomly selected to run the 5K fun run. Round all answers to 4 decimal places where possible 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 probability that this runner's time will be between 20.2599 and 21.0599 minutes.
  5. For the 13 runners, find the probability that their average time is between 20.2599 and 21.0599 minutes.
  6. Find the probability that the randomly selected 13 person team will have a total time less than 266.5.

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Expert Solution

orchestra answered 1 year ago
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