Question

At a taxi-stop on a busy street, the inter-arrival times of taxis dropping off passengers (and...

At a taxi-stop on a busy street, the inter-arrival times of taxis dropping off passengers (and then being ready for the pick up) have a mean 5 minutes with a standard deviation 1 minute. The taxis are not allowed to wait for customers at the stop. Customers arrive at the stop in a Poisson process once every 6 minutes on the average.

(a) Determine the expected number of customers waiting, when a taxi leaves the stop.

(b)What is the probability that there would be no waiting customer, when a taxi leaves the stop?

(c) Determine the mean waiting time of a customer.

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