a) Find the probability of the number of arrivals (0-5) during i) a 15 minute interval...

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a) Find the probability of the number of arrivals (0-5) during i) a 15 minute interval and ii) a 30 minute interval. b) Probability that the system is idle. [3 Marks] [3 Marks] c) Calculate the expected number of customers in the tailor shop. [3 Marks] d) Compute the calculate the expected waiting time in the queue. [3 Marks] e) Derive the expected number of customers in the queue. [3 Marks] A tailor specializes in ladies dresses. The number of customers approaching the tailor appear to be Poison distributed with a mean of six customers per hour. The tailor attends to customers on a first-come-first-served basis and the customers wait if need be. The tailor can attend to the customers at an average rate of ten customers per hour with service time exponentially distributed. a) Find the probability of the number of arrivals (0-5) during i) a 15 minute interval and ii) a 30 minute interval. b) Probability that the system is idle. [3 Marks] [3 Marks] c) Calculate the expected number of customers in the tailor shop. [3 Marks] d) Compute the calculate the expected waiting time in the queue. [3 Marks] e) Derive the expected number of customers in the queue. [3 Marks] A tailor specializes in ladies dresses. The number of customers approaching the tailor appear to be Poison distributed with a mean of six customers per hour. The tailor attends to customers on a first-come-first-served basis and the customers wait if need be. The tailor can attend to the customers at an average rate of ten customers per hour with service time exponentially distributed.

Answer rating: 100% (QA)

a To find the probability of the number of arrivals 05 during a given time interval we can use the Poisson distribution formula The Poisson distributi... View the full answer