Question

Question 32 (1 point) A dental clinic at which only one dentist works is open only 4 days a week. During those 4 days, the traffic is uniformly busy with patients arriving at the rate of 3.9 per hour. The doctor serves patients at the rate of 1.2 every 10 minutes. During those 4 days that the clinic is operating, what is the probability that the clinic is empty (except for the dentist)? Note: 1- This probability needs to be expressed as a number between 0 and 1. 2- Only round your final answer. Round your final to 2 decimal places. Your Answer: Answer

Answer 1

Answer

This is an example of Single Server Queuing Model

$\small \lambda = Arrival\, \, Rate = 3.9\, \, per \, \, hour$

$\small \mu = Service\, \, Rate = 1.2 \, \, per\, \, 10\, \, min\, \, =7.2\, \, per \, \, hour$

Probability of the clinic is empty (P0) is a probability that there is no customer in the system

$\small P_0 = 1 -\lambda/\mu = 1 - (3.9/7.2) =1- 0.5417 = 0.4583 \approx 0.46$