a) A university wishes to conduct a study of the average summer earnings of its students.The university wants to be 95% confident that the estimated mean is with $50 of the actual population mean.Assuming that the population standard deviation is $400, what sample size is needed to achieve this objective?

b) A marketing firm wants to determine the proportion of Americans who have travelled to Europe and would like to be 95% confident that it is able to be within 0.03 (3%) of the true population mean.If the sample proportion is 0.24, what is the sample size needed to achieve this objective?