County General Hospital’s cardiac care unit (CCU) has seven beds, which are virtually always occupied by patients who have just undergone heart surgery. Two registered nurses are on duty at the CCU in each of the three 8-hour shifts. On average, a patient requires a nurse’s attention every 66 minutes. The arrival rate follows a Poisson distribution. A nurse will spend an average of 19 minutes (exponentially distributed) assisting a patient and updating medical records regarding the care provided.
(a) What percentage of the nurses’ time is spent responding to these requests?
(b) What is the average time a patient spends waiting for one of the nurses to arrive at bedside?
(c) What is the average number of patients waiting for a nurse to arrive?
(d) What is the probability that a patient will not have to wait for a nurse to arrive?