The rate of arrival of customers at a public telephone follows Poisson distribution, with an average time
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The rate of arrival of customers at a public telephone follows Poisson distribution, with an average time of ten minutes between one customer and the next. The duration of a phone call is assumed to follow exponential distribution with a mean time of three minutes.
(i) What is the probability that a person arriving at the booth will have to wait?
(ii) What is the average length of the queue?
(iii) The Mahanagar Telephone Nigam Ltd. will install another booth when it is convinced that the customers would have to wait for at least three minutes for their turn to make a call. How much should be the flow of customers in order to justify a second booth?
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