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Problem

Suppose that the times between arrivals at a bank during the peak period of the day are exponentially distributed with a mean of 45 seconds. If you just observed an arrival, what is the probability that you will need to wait for more than a minute before observing the next arrival? What is the probability you will need to wait at least two minutes?

Step-by-step solution

The times between arrivals at a bank during the peak period of the day are exponentially distributed with the mean of .

That is, per second.

Since is the rate per seconds then the rate per minutes is .

That is,

Comment

Let denotes the inter arrival time at a bank during the peak period of the day are exponentially distributed with a mean of .

That is,

The probability that one has to wait for more than a minute before observing the next arrival is,

The required probability can be obtained by using the Excel Statistical function .

Therefore, the probability that one has to wait for more than a minute before observing the next arrival is

Comment

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The probability that you will need to wait at least two minutes is,

Therefore, the probability that you will need to wait at least two minutes is

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