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. P0= What is the average number of requests that will be waiting for service? If required, round your answer to four decimal places. Lq= What is the average waiting time in minutes before service begins? If required, round your answer to nearest whole number. Wq=
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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.
P0= - What is the average number of requests that will be waiting for service? If required, round your answer to four decimal places.
Lq= - What is the average waiting time in minutes before service begins? If required, round your answer to nearest whole number.
Wq= - What is the average time at the reference desk in minutes (waiting time plus service time)? If required, round your answer to nearest whole number.
W= - What is the probability that a new arrival has to wait for service? If required, round your answer to four decimal places.
Pw=
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
