Explain the central limit theorem in the context of the current problem, and indicate whether it was needed to find these probabilities in a, b, and c (might differ for each of a, b, and c).

  1. It is known that the population of students who take EconS 311 have a final grade that is normally distributed with µx = 81 and sx2 = 25.
  2. For one observation (student) from this population, find

 

Now suppose that a random sample of students is selected from this population.  Note that the next two questions are about, not about X itself.

  1. In a random sample of size n = 64, find
  2. In a random sample of size n = 36, find
  3. Explain the central limit theorem in the context of the current problem, and indicate whether it was needed to find these probabilities in a, b, and c (might differ for each of a, b, and c).

 

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