A company has three subdivisions, employing a total of 970 managers. Independent random samples of managers were taken from each subdivision, and the number of years with the company was determined for each sample member. The results are summarized in the accompanying table.

a. Find a 99% confidence interval for the mean number of years with the company for managers in subdivision 1.
b. Find a 99% confidence interval for the mean number of years with the company for all managers.

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Subdivision 1 352 30 9.2 4.9 Subdivision 2 Subdivision 3 287 331 20 12.3 6.4 30 13.5 7.6