Answer:
The probability of no arrivals in a one-minute period is 0.002479.
Step-by-step explanation:
We are given that Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The mean arrival rate is 6 passengers per minute.
The above situation can be represented through Poisson distribution because a random variable which includes the arrival rate is considered as Poisson random variable.
The Probability distribution function for Poisson random variable is ;
where, = arrival rate
<em />
<em>Let X = Arrival of Airline passengers</em>
The mean of the Poisson distribution is given by = E(X) = , which is given to us as 6 passengers per minute.
So, X ~ Poisson ()
Now, the probability of no arrivals in a one-minute period is given by = P(X = 0)
P(X = 0) =
=
= 0.002479
<u><em>Hence, the probability of no arrivals in a one-minute period is 0.002479.</em></u>