The Fed is making predictions for what they think headline inflation will be in June 2016. They sample81 forecasters. It is known that the standard deviation is 1.02 basis points.

(a) Suppose the average of the sample were 2.25 percent. What is the probability that an individualinflation prediction is higher than 2.5 percent? What is the probability that it is between 1.7 and2.3 percent?

(b) Consider the sampling distribution. What is the mean of this distribution and what is the standarddeviation?

(c) What is the probability that the average prediction of a sample of 81 forecasters will be higherthan 2.5 percent?

(d) Suppose you survey 81 professional forecasters and find that the mean is 2.45 percent. Constructa 95 and 99 percent confidence intervals for the mean of the population. Does the actual meanfall within the confidence interval?

(e) What are the margins of error for the confidence intervals, and how would they change as yousampled more forecasters?