1.It is known that the population of students who take THIS CLASS have a final grade that is normally distributed with x = 81 and x^2 = 25

a.For one observation (student) from this population, find (X<80)

Now suppose that a random sample of students is selected from this population.Note that the next two questions are X#about, 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

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).