Question

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

a. Compute the probability of no arrivals in a one-minute period (to 6 decimals).

b. Compute the probability that three or fewer passengers arrive in a one-minute period (to 4 decimals).

c. Compute the probability of no arrivals in a -second period (to 4 decimals).

d. Compute the probability of at least one arrival in a -second period (to 4 decimals).

Answer 1

Answer:

Given that:

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

The mean arrival rate and no arrival period is not given. So i will give example with mean = 10 and no arrival in a 15 second period.

The Poisson probability formula is

a) Compute the probability of no arrivals in a one-minute period

probability of no arrivals in a one-minute period is

b) Compute the probability that three or fewer passengers arrive in a one-minute period

Add the corresponding probabilities

c) Compute the probability of no arrivals in a -second period

The expected number of occurrences in 15 seconds is the mean of 1 minute multiplied by the number of minutes.

Evaluate the formula for k=0 and

d) Compute the probability of at least one arrival in a -second period

Use the complement rule