A manager examined data flow diagrams in a small portion of system development projects and determined that there were nearly 12.5% of them with errors. His boss, the Vice-President for Systems Development wants a better estimate of the percentage so you are tasked to sample the diagrams produced for the past five years and report back.

a) How large a sample would one have to examine to be 99% certain that the estimate would be within 3% of the actual percentage? Explain the steps to the answer.

b) Given the answer to part a), explain how the estimate was gotten that will be reported back to the vice-president