A company is interested in estimating p, the mean number of days of sick leave taken by all its employees. The firm's statistician selects at random 100 personnel files and notes the number of sick days taken by each employee. The following sample statistics are computed:  = 12.2 days, 5 = 10 days.
a. Estimate µ using a 90% confidence interval. Interpret the result.
b. How many personnel files would the statistician have to select in order to estimate µ to within 2 days with a 99% confidence interval?
c. Estimate σ using a 90% confidence interval. Interpret the result.