# The emergency room of the community hospital in Farmburg has one receptionist, one doctor, and one nurse.

## Question:

The emergency room of the community hospital in Farmburg has one receptionist, one doctor, and one nurse. The emergency room opens at time zero, and patients begin to arrive some time later. Patients arrive at the emergency room according to the following probability distribution:

**Time Between**

**Arrivals (min.) …… Probability**

5 ………………………… .06

10 ………………………… .10

15 ………………………… .23

20 ………………………… .29

25 ………………………… .18

30 ………………………… .14

1.00

The attention needed by a patient who comes to the emergency room is defined by the following probability distribution:

**Patient Needs**

**to See ………………………… Probability**

Doctor alone ………………………… .50

Nurse alone ………………………… .20

Both …………………….............…… .30

1.00

If a patient needs to see both the doctor and the nurse, he or she cannot see one before the other—that is, the patient must wait to see both together.

The length of the patient’s visit (in minutes) is defined by the following probability distributions:

Simulate the arrival of 20 patients to the emergency room and compute the probability that a patient must wait and the average waiting time. Based on this one simulation, does it appear that this system provides adequate patient care?

## Step by Step Answer:

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