Question

Problem 7 You're a healthcare engineering consultant and you're analyzing the emergency room design at Pawhuska Hospital, Inc. To understand the service rate of the ER, you must first analyze the arrival of patients, and you begin by studying the overnight arrivals. The probability distribution is shown in the table. Plot the probability distribution function of hourly patients arriving to the ER Calculate the mean and standard deviation of the probability distribution of hourly ER arrivals What is the probability that fewer than three patients arrive in an hour? a. b. c. Arrivals to the ER in an hour during the night shift Probability 1 0.04 0.11 0.24 0.32 0.14 0.08 0.02 0.05 2 34 5 6 7

Answer 1

(a) Plot ofprobability distribution function 0.35 0.3 0.25 0.2 2 0.15 0.05 Patients arriving to the ER Arrival to Probabilityx**P(x) x2*P(x) the ER (x) P(x) 0.04 0.11 0.24 0.32 0.14 0.08 0.02 0.05 0 0.11 0.48 0.96 0.56 0.4 0.12 0.35 2.98 0.11 0.96 2.88 2.24 2 0.72 2.45 11.36 4 Total

Mean= E(X) =Σ x * P (x) = 2.98 Standard deviation-SD(X) ,IE (X2)-(E(X))2 Now E (X2)-Ix2*P(x) 11.36 SD(X)-、11 1.36-(2.98)2イ11.36-8.8804 2.4796 1.5747 (c) The probability that fever than three patients arrive in hour P(X<3) P(X-0)+P(X-1)+P(X-2) 0.04+0.11 +0.24 PX<3)0.39