Question

Each airline passenger and his/her luggage must be checked for security reasons. Suppose that at RDU, an average of 10 passenger/minute arrive (exponentially distributed) at the security checkpoint consisting of a metal detector and x-ray machine. The checkpoint can process an average of 12 passengers per minute (exponentially distributed). a. What is the probability that a passenger will wait before going through the checkpoint? b. On average, how many passengers will be waiting in line to enter the checkpoint? c. On average, how long will a passenger spend at the checkpoint (waiting and being processed)?

Answer 1

Answel- Given that fach airline passengel and his/hel luggage . * An avelage of lo passenger / minute allive. k. The check point can neocess an avel 12 pan engel pel minute. se A - Mood P (a passenger has to wait ) = l-Po El- = 1-= %5011667 Aveeg. of passen gee on the waiting Sue to entee the check point 12 (6) u Crear) 12 (12-10) 100 – u 1667 passenger spend at checkpoint @. = of U Avelage = = 10 MM- Ovu 1667