Question

Patients arrive at Max hospital for X-ray according to a Poisson process. There is an X-ray machine and arriving patients form a single line that feeds the X-ray machine in a first-come-first-served order. Past data show that the average wait for a patient is 30 minutes. The service time in the process takes, on an average, 10 minutes, exponentially distributed.  

NOTE: 1-4 HAVE ANSWERS, I ONLY NEED 5-6-7

1- Average number of patients in the system

Group of answer choices

a-4

b-3 (Correct Answer)

c-2

d-4/3

2-Average number of patients in the queue

Group of answer choices

a-9/2

b-3/4

c-9/4 (Correct Answer)

d-3

3-Average time a patient spends in the system

a-3/4 hours

b-2/3 hours (Correct Answer)

c-1/4 hours

d-2 hours

4-What is the arrival rate?

a-9/2 patients/hr (Correct Answer)

b-3/2 patients/hr

c-9/4 patients/hr

d-5 patients/hr

5-Probability that there is at least one patient in the system

a-75%

b-45%

c-55%

d-25%

6-Probability that there are less than or equal to 3 patients in the system

a-1 - (λ / μ)^4

b-1 - (λ / μ)^3

c-(λ / μ)^4

d-(λ / μ)^3

7-Probability that there are more than or equal to 2 but less than or equal to 3 patients in the system

Group of answer choices

a-(λ / μ)^3 - (λ / μ)^4

b-(λ / μ)^3 - (λ / μ)^2

c-(λ / μ)^2 - (λ / μ)^4

d-(λ / μ)^4 - (λ / μ)^2

Answer 1

we have Arrival rated)= 9/2 patients/ bo Service gate (ll) 6 patients/ho 60 5 10 5) probability of atleast one patient in the System -PEND patient in the system) |- (1-9).*CA l 972 6. 11 9 12 0.75 E 75% .: al 75% is correct Answer. let 6) poobability that there are dess dban ao equal 30 patients in the system .. Sede baffi fintensity - poobability = (1-3) (1+3+s4=$*] = (1-5) [ 1-39 = 1.84 1-4 .:option @ cis concert option as - 4 is correct

*) probability that there are more than or equal stó 2 but but less than or equal to 3 patient 3 in the system 2625x53) = P(x=2) + PCX =3) (1-3)*82 + (1-3) 83 (1-5) * [ $?+ 93] (1-5) 32 its] 2 c (1-8282 82-84 we - (A) .: Option Es HP file is comect choice 2