Mr. Duke wants to estimate the production days that would be lost during the next three months by sampling the vacation

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Mr. Duke wants to estimate the production days that would be
lost during the next three months by sampling the vacation
intentions of a sample of employees. Mr. Duke randomly selects 36
employees in the organization and finds that the average number of
days they intend to take off is 16 days during the coming three
summer months, with a standard deviation of seven (7) days.
Based on these sample statistics, Mr.
Duke wants to estimate at a 99% confidence level, the days that
will be lost because of the entire population of workers taking
vacation time during the next three months, so that the plant
manager knows how much temporary help he should plan on hiring
during the summer months in order for work to proceed smoothly.
Assume that days of intending to take vacation by an employee is
independent of all other employees’ vacation intentions.