As an Aid to the Establishment of Personnel Requirements,the Director $\bar { X }$

As an aid to the establishment of personnel requirements,the director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during a 24-hour period.The director randomly selects 64 different 24-hour periods and determines the number of admissions for each.For this sample, $\bar { X }$ = 19.8 and S² = 25.Using the sample standard deviation as an estimate for the population standard deviation,what size sample should the director choose if she wishes to estimate the mean number of admissions per 24-hour period to within 1 admission with 99% reliability?