A 2012 Gallup Poll reported that only 581 out of a total of 2004 U.S. adults said they had a “great deal of confidence” or “quite a lot of confidence” in the public school system. This was down 5 percentage points from the previous year. Assume the conditions for using the CLT are met.

a. Find a 99% confidence interval for the proportion that express a great deal of confidence or quite a lot of confidence in the public schools, and interpret this interval.

b. Find a 90% confidence interval and interpret it.

c. Find the width of each interval by subtracting the lower proportion from the upper proportion, and state which interval is wider.

d. How would a 95% interval compare with the others in width?