It was reported that, in a sample of 507 adult Americans, only 142 correctly described the Bill of Rights as the first ten amendments to the U.S. Constitution.

Calculate a (two-sided) confidence interval using a 99% confidence level for the proportion of all U. S. adults that could give a correct description of the Bill of Rights.

**Determine the sample size for determining the populating proportion of problem 4, if the margin of error is kept to plus or minus 5% with a confidence interval of 90%***