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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.

Respuesta :

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

Step-by-step explanation:

Since we have given that

Arrival rate = [tex]\lambda=10/hour[/tex]

Service rate = [tex]\mu=12/hour[/tex]

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

[tex]p_0=1-\dfrac{\lambda}{\mu}\\\\p_0=1-\dfrac{10}{12}\\\\p_0=1-\dfrac{5}{6}\\\\p_0=\dfrac{6-5}{6}\\\\p_0=\dfrac{1}{6}[/tex]

[tex]p_0=0.1667[/tex]

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

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