airline passengers arrive randomly and independently at the passenger screening facility at an airport. The mean arrival rate is 10 passengers per minute. What is the probability of no arrivals in a 15 second period.

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- October 23rd 2007, 10:26 AMdcliftairline probability
airline passengers arrive randomly and independently at the passenger screening facility at an airport. The mean arrival rate is 10 passengers per minute. What is the probability of no arrivals in a 15 second period.

- October 23rd 2007, 02:41 PMCaptainBlack
The number of arrivals in a time interval of length has a Poisson distribution with expected number where is the expected number per unit time.

Here the expected numbe per unit time is of an arrival per second, so the expected number in seconds is .

Hence the probability of arrivals in a second interval is:

so if , this is:

RonL