Home/Business
/Patients arrive randomly at an eye care clinic for eye exam. Suppose that there is only one optometrist. The time required for the exam varies from patient to patient. Arrival rates have been found to follow the Poisson distribution (i.e., exponentially distributed inter-arrival times), and the service times follow the exponential distribution. The average arrival rate is 10 patients per hour, and the average service rate is 16 patients per hour. On arrival, a patient needs to stay in the waiting room until the optometrist becomes available. Once the optometrist is available, the next patient goes to the examination room for the eye exam. How many patients, on the average, will be in the examination room? Note: Keep two decimal places for your answer.

Question
Patients arrive randomly at an eye care clinic for eye exam. Suppose that there is only one optometrist. The time required for the exam varies from patient to patient. Arrival rates have been found to follow the Poisson distribution (i.e., exponentially distributed inter-arrival times), and the service times follow the exponential distribution. The average arrival rate is 10 patients per hour, and the average service rate is 16 patients per hour. On arrival, a patient needs to stay in the waiting room until the optometrist becomes available. Once the optometrist is available, the next patient goes to the examination room for the eye exam. How many patients, on the average, will be in the examination room? Note: Keep two decimal places for your answer.

NFX5IJThe Asker · Management

Transcribed Image Text: Patients arrive randomly at an eye care clinic for eye exam. Suppose that there is only one optometrist. The time required for the exam varies from patient to patient. Arrival rates have been found to follow the Poisson distribution (i.e., exponentially distributed inter-arrival times), and the service times follow the exponential distribution. The average arrival rate is 10 patients per hour, and the average service rate is 16 patients per hour. On arrival, a patient needs to stay in the waiting room until the optometrist becomes available. Once the optometrist is available, the next patient goes to the examination room for the eye exam. How many patients, on the average, will be in the examination room? Note: Keep two decimal places for your answer.

More

Transcribed Image Text: Patients arrive randomly at an eye care clinic for eye exam. Suppose that there is only one optometrist. The time required for the exam varies from patient to patient. Arrival rates have been found to follow the Poisson distribution (i.e., exponentially distributed inter-arrival times), and the service times follow the exponential distribution. The average arrival rate is 10 patients per hour, and the average service rate is 16 patients per hour. On arrival, a patient needs to stay in the waiting room until the optometrist becomes available. Once the optometrist is available, the next patient goes to the examination room for the eye exam. How many patients, on the average, will be in the examination room? Note: Keep two decimal places for your answer.

Community Answer

XQFCHK

false

1. UNITS IN THE SYSTEM(LS) = ARRIVAL RATE / (SERVICE RATE - ARRIVAL RATE) = 10 / (16 - 10) = 1.67   ... See the full answer