Q4. An independent random sample of = 100 observations was taken from a large population which has a mean of = 80 and a variance of 2 = 169.

A. Use Chebychev's theorem to determine the minimum probability that the sample mean lies between 77.4 and 82.6. (3 points)

B. Apply the central limit theorem to determine the probability that the sample mean lies between 77.4 and 82.6. Is the central limit theorem applicable in this case? (3 points)

C. What would happen to the probability in part (B) if the sample size were to fall to 50? (2 points)

D. Provide a graph which shows the sampling distributions where =100and where = 50 in order to illustrate your answer to part (B) and part (C). (2 points)