Question

In: Statistics and Probability

The reference desk of a university library receives requests for assistance. Assume that a Poisson probability...

The reference desk of a university library receives requests for assistance. Assume that a Poisson probability distribution with an arrival rate of 11 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 15 requests per hour. (Round your answers to four decimal places.)

(a)

What is the probability that no requests for assistance are in the system?

(b)

What is the average number of requests that will be waiting for service?

(c)

What is the average waiting time (in hours) before service begins?

h

(d)

What is the average time (in hours) at the reference desk (waiting time plus service time)?

  h

(e)

What is the probability that a new arrival has to wait for service?

Solutions

Expert Solution

It is given that the arrival rate follows poisson distribution with arrival rate 11 request per hour and service time follows exponential distribution with service rate 15 request per hour.

,

a. The probability that no requests for assistance are in the system=

(b) The average number of requests that will be waiting for service

  

The average number of requests that will be waiting for service is 2.7496

(c) The average waiting time (in hours) before service begins is

The average waiting time (in hours) before service begins is 0.1344 hours

(d) The average time (in hours) at the reference desk (waiting time plus service time) is

The average time (in hours) at the reference desk (waiting time plus service time) is 0.2011 hours

(e)The probability that a new arrival has to wait for service mean there are more than one customer in the system i.e

  

The probability that a new arrival has to wait for service mean there are more than one customer in the system 0.5377


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