A 2017 Gallup poll reported that 658 out of 1028 U.S. adults believe that marijuana should be legalized. When Gallup first polled U.S. adults about this subject in 1969, only 12% supported legalization. Assume the conditions for using the CLT are met.

a. Find and interpret a 99% confidence interval for the proportion of U.S. adults in 2017 that believe marijuana should be legalized.

b. Find and interpret a 95% confidence interval for this population parameter.

c. Find the margin of error for each of the confidence intervals found in parts a and b.

d. Without computing it, how would the margin of error of a 90% confidence interval compare with the margin of error for the 95% and 99% intervals? Construct the 90% confidence interval to see if your prediction was correct.