Airline passengers arrive randomly and independently at the passenger screening

Question

Airline passengers arrive randomly and independently at the passenger screening facility at a major international airport. The mean arrival rate is 8 passengers per minute.

What is the probability of no arrivals in a 1-minute period? If required, round your answer to six decimal places.

What is the probability of 3 or fewer arrivals in a 1-minute period? If required, round your answer to six decimal places.

What is the probability of no arrivals in a 18-second period? If required, round your answer to four decimal places.

What is the probability of at least 1 arrival in a 18-second period? If required, round your answer to four decimal places.

Explanation / Answer

This is an example of a Poisson distribution.
The number of arrivals in 1 minute = X
X = P(8)

a. What is the probability of no arrivals in a 1-minute period?
p(X = 0) = e^(-)
= 0.00034

b. What is the probability of 3 or fewer arrivals in a 1-minute period?
p(X 3) = F(3)
= 0.0424

c. What is the probability of no arrivals in a 15-second period?
In 15 seconds X is Po(3)
p(X = 0) = e^(-3)
= 0.0286

d. What is the probability of at least 1 arrival in a 15-second period?
p(X 1) = 1 - p(X = 0)
= 1 - 0.0286
= 0.9714

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