A Company Is Interested in Estimating $$\mu$$ , the Mean Number of Days of Sick Leave Taken

Multiple Choice

A company is interested in estimating $$\mu$$ , the mean number of days of sick leave taken by its employees. The firm's statistician randomly selects 100 personnel files and notes the number of sick days taken by each employee. The sample mean is 12.2 days. From historical records, the population standard deviation is about 10 days.
-How many personnel files would the director have to select in order to estimate $\mu$
To within 2 days with 99% confidence?

A) 2
B) 13
C) 136
D) 165
E) 166