Breezy Analytics has been hired investigate a set of issues, which will require collecting some sample information. You have been asked to determine the sample size needed to tackle these issues.

a) Barbados Statistical Service hires Breezy Analytics to help them estimate a 98% confidence interval for the average income of all accountants in Barbados. The population standard deviation is known to be $1,000. What sample size would be needed so the margin of error will be approximately $50.

b) A member of the house of parliament is interested in attaining a 99% confidence interval for the population of all Barbadians who will cheat on their taxes. If they want the margin of error to be 0.01, what sample size would be needed?