An immigration officer at Heathrow Airport in London can on the average process

Question

An immigration officer at Heathrow Airport in London can on the average process (serve) 15 arriving passengers every hour. If on the average 12 passengers arrive per hour at her station, then: The probability that an arriving passenger will have to wait for this immigration officer is The average number of entrants (passengers) in line waiting for the immigration officer is On average, the amount of time, in minutes, spent by a passenger in the entire immigration system, waiting and being processed, would be The probability that there are 4 or more people in the system. The probability that the time spent waiting in line will exceed 20 minutes.

Explanation / Answer

3). 8 or 80%

12/15=.8

4). 3.2

Iqueue=TR*Timeline
Timeline=20min-4=16 min
16/60=.267

5). 20 minutes

1/(mu-sigma)=FT
1/(15-12)=1/3hr=20 min

6). .4096

(signma/mu)^4=(12/15)^4=.4096

7). .2943

(12/15)e^(-15(1-(12/15))(20/60))

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