An Administrator in a Comprehensive Hospital Believes Certain Departments Are $\begin{array}{cc}\text { Time Between Arrivals (minutes) }&\text { Probability }\\30 & 0.20 \\60 & 0.40 \\90 & 0.30 \\120 & 0.10\end{array}$

Essay

An administrator in a comprehensive hospital believes certain departments are overstaffed and others are understaffed. In many departments, a patient's arrival is quite variable and the time required to treat that patient is also quite variable. In fact, the administrator does not believe there is a mathematical relationship between arrivals and treatment time.Like most hospitals, this one has kept extensive records for each patient. It uses this data for a simulation to determine proper staffing levels for its various departments. The administrator decides to test the procedure with data from the Maternity Center. The following table represents the best probability forecast of Maternity Center arrivals. $\begin{array}{cc}\text { Time Between Arrivals (minutes) }&\text { Probability }\\30 & 0.20 \\60 & 0.40 \\90 & 0.30 \\120 & 0.10\end{array}$ Historic data also indicates that 90% of Maternity Center arrivals are admitted and 10% are sent home due to false labor. The following table represents the historic frequency distribution for the time a patient spends in the labor room. $\begin{array}{ll}\text { Time in Labor Room (hours) }&\text { Probability }\\0.5 & 0.10 \\1.0 & 0.10 \\2.0 & 0.30 \\4.0 & 0.30 \\5.0 & 0.20\end{array}$ The administrator now believes the use of past data is an excellent indicator of future conditions.
a. Determine the third patient's arrival time given the following random numbers: 12, 77, 53, 07, 01, 34, 76, 20, 19, and 85. The simulation starts at 8:00 a.m. with the first arrival coming after 8:00 a.m.
b. Determine the eighth patient's arrival time given the following random numbers: 12, 77, 53, 07, 01, 34, 76, 20, 19, and 85. The simulation starts at 8:00 a.m. with the first arrival coming after 8:00 a.m.
c. 90% of Maternity Center patients are admitted to the hospital and 10% are sent home (see the table below). Given this information, determine the number of patients admitted using the following random numbers: 89, 50, 03, 52, 79, 38, 24, 61, 28, and 27.
d. Determine when the third patient will leave the labor room using the following random numbers: 97, 49, 13, 41, 82, 38, 16, 82, 13, and 22 for labor room stays.
e. Determine when the eighth patient will leave the labor room using the following random numbers: 97, 49, 13, 41, 82, 38, 16, 82, 13, and 22 for labor room stays.
f. Determine the average time a woman spends in the labor room using the following random numbers: 97, 49, 13, 41, 82, 38, 16, 82, 13, and 22 for labor room stays.