Question

Problem 15-5 The reference desk of a university library receives requests for assistance. Assume that a Poisson probability distribution with an arrival rate of 10 requests per hour can be used to describe the arrival pattern and that service times follow an exponential probability distribution with a service rate of 12 requests per hour. What is the probability that no requests for assistance are in the system? If required, round your answer to four decimal places.

Answer 1

Answer: The probability that no requests for assistance are in the system is 0.1667.

Explanation:

Since we have given that

Arrival rate =
`\lambda=10/hour`

Service rate =
`\mu=12/hour`

the probability that no requests for assistance are in the system is given by

`p_0=1-(\lambda)/(\mu)\\\\p_0=1-(10)/(12)\\\\p_0=1-(5)/(6)\\\\p_0=(6-5)/(6)\\\\p_0=(1)/(6)`

`p_0=0.1667`

Hence, the probability that no requests for assistance are in the system is 0.1667.