Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The mean arrival rate is 10 passengers per minute. 1. Compute the probability of no arrivals in a one-minute period. 2. Compute the probability that three or fewer passengers arrive in a one-minute period. 3. Compute the probability of no arrivals in a 15-second period. 4. Compute the probability of at least one arrival in a 15-second period.

1. 0.0000454

2. 0.01034

3. 0.0821

4. 0.918

Step-by-step explanation:

Let X be the random variable denoting the number of passengers arriving in a minute. Since the mean arrival rate is given to be 10,  

1. Requires us to compute

2.  We need to compute

3. The expected no. of arrivals in a 15 second period is = . So if Y be the random variable denoting number of passengers arriving in 15 seconds,

4. Here we use the fact that Y can take values . So, the event that "Y is either 0 or 1" is a sure event ( i.e it has probability 1 ).

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step-by-step explanation:

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step-by-step explanation: