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Word File Edit View Insert Format Tools Table Window Help HW 8 [Compatibility Mode] Q Search in Document Home Insert Design Layout References Mailings Review View Share ^ AaBbCcDdEe AaBbCcDcAaBbCcDdE Paste No SpaingHeading1 1HeadingTitle 1) Patients arrive to a hospital emergency room at a rate of 2 per hour according to a Poisson process. A doctor works a 12-hour shift from 6 a.m. until 6 p.m. Answer a) If the doctor has seen six patients by 8 am., what is the probability that the b) What is the expected time between the arrival of successive patients? What is the following questions doctor will see a total of nine patients by 10 a.m.? the probability that the time between the arrival of successive patients will be more than 1 hour? c)Of patients admitted to the emergency room, 14% are classified as "urgent." What is the probability that the doctor will see more than three "urgent" patients during her shift? d) The hospital also has a walk-in clinic to handle minor problems. Patients arrive at this clinic at a rate of 4 per hour. What is the probability that the total number of patients arriving at both the emergency room and clinic from 6 a.m until 12 noon will be 30? Page 1 of1 180 Words English (US) Focus + 150%

Explanation / Answer

Question 1

Here patient arrival rate = 2 per hour

(a) Here the poisson process has memoryless propoerty so as we know that till 8 a.m. there are 6 patients. So, there are 3 patients who will come in between 8 am to 10 a.m. so in next 2 hour, there are expected number of 4 patients.

so, Pr( X = 3) = POISSON (X =3; 4) = e-3 34 /4! = 0.1954

(b) Here the expected time to arrival between two patients = 1/2 = 30 minutes = half an hour

Heree Pr( t > 1 hour) when mean time = 1/2 hour here the time distribution is exponential

so, Pr(t > 1 hour ) = 1 - (1 - e-1) = e-1  = 0.3679

(c) Here expected number of urgent patients will arrive during his shifts = 12 * 2 * 0.14 = 3.36

If number of urgent patients are X

Pr (X > 3 ) = POISSON (X >3 ; 3.36) = 0.4329

(d) Here we will add both poisson variables

where Total expected number of patients from 6 am to 12 pm = expected Patients in emergency + expected patients for minor treatments = 6 * 2 + 6 * 4 = 36 patients

so Here we have to find Pr(X = 30) = POISSON (X = 30; 36) = 0.0427

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