As an aid in 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 49 different 24-hour periods and determines the number of admissions for each. For this sample, x = 18.4 and we know that the population variance is 16. Estimate the mean number of admissions per 24-hour period with a 95% confidence interval.