Suppose a Large Labor Union Wishes to Estimate the Mean $\bar { x } = 7.5$

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 348 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 $\bar { x } = 7.5$ hours and $s = 3.5$ hours, find a $99 \%$ confidence interval for the true mean number of hours a union member is absent per month. Round to the nearest thousandth.

A) $7.5 \pm .258$
B) $7.5 \pm .026$
C) $7.5 \pm .483$
D) $7.5 \pm .186$