Question

Problem 3-17 (Algorithmic) 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. A)

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

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

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

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

Answer 1

X ~ Poisson ()

Poisson probability distribution is

P( X = x) = e^-X / X!

a)

= 8 per min

P( X = 0) = e^-8  

= 0.000335

b)

P( X <= 3) = P( X = 0) +P( X = 1) +P( X = 2) +P( X = 3)

= e^-8 + e^-8 * 8 + e^-8 * 8² / 2! + e^-8 * 8³ / 3!

= 0.042380

c)

For 18 second period,

= 8 * 18 / 60 = 2.4

P(X = 0) = e^-2.4

= 0.0907

d)

P( X >= 1) = 1 - P( X = 0)

= 1 - 0.090718

= 0.9093