Suppose a Large Labor Union Wishes to Estimate the Mean $\bar { x } = 8.1$

Suppose a large labor union wishes to estimate the mean number of hours per month a union member is absent from work. The union decides to sample 406 of its members at random and monitor the working time of each of them for 1 month. At the end of the month, the total number of hours absent from work is recorded for each employee. If the mean and standard deviation of the sample are $\bar { x } = 8.1$ hours and $s = 2.3$ hours, find a $99 \%$ confidence interval for the true mean number of hours a union member is absent per month. Rotund to the nearest thousandth.
A) $8.1 \pm .294$
B) $8.1 \pm .015$
C) $8.1 \pm .194$
D) $8.1 \pm .113$