Many of a bank

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s customers use its automatic teller machine to transact business after normal banking hours. During the early evening hours in the summer months, customers arrive at a certain location at the rate of one every other minute. This can be modeled using a Poisson distribution. Each customer spends an average of $92$seconds completing his or her transactions. Transaction time is exponentially distributed.

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$$Determine the probability that a customer will not have to wait upon arriving at the automatic teller machine.