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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.
a. For one observation (student) from this population, find Pr (X < 80).
Now suppose that a random sample of students is selected from this population. Note that the next two questions are about X‾, not about X itself.
b. In a random sample of size n = 64, find Pr (X < 80).
c. In a random sample of size n = 36, find Pr (78< X < 84).
d. 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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Include a cover page containing the title of the assignment, the student's name, the professor's name, the course title, and the date. The cover page and the reference page are not included in the required page length.
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