A firm employs 189 junior accountants. In a random sample of 50 of these, the mean number of hours overtime billed in a particular week was 9.7, and the sample standard deviation was 6.2 hours.
a. Find a 95% confidence interval for the mean number of hours overtime billed per junior accountant in this firm that week.
b. Find a 99% confidence interval for the total number of hours overtime billed by junior accountants in the firm during the week of interest.