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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.

1. For one observation (student) from this population, find $C:\Users\ADMINI~1\AppData\Local\Temp\ksohtml\wpsBC2D.tmp.png$

Now suppose that a random sample of students is selected from this population. Note that the next two questions are about $C:\Users\ADMINI~1\AppData\Local\Temp\ksohtml\wpsBC2E.tmp.png$ , not about X itself.

1. In a random sample of size n = 64, find $C:\Users\ADMINI~1\AppData\Local\Temp\ksohtml\wpsBC3F.tmp.png$

1. In a random sample of size n = 36, find $C:\Users\ADMINI~1\AppData\Local\Temp\ksohtml\wpsBC40.tmp.png$

1. 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).