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The federal government is undertaking a massive process analysis of the notoriously chaotic border Santa Barbara and Tijuana. They have selected the San Ysidro station as a sample case and would like your input in doing the following analysis. Automobiles arrive from Mexico at the rate of 20 per hour according to a Poisson distribution. The station has 3 inspection lanes for cars and 1 inspection lane for trucks. All cars join a common queue and go to the first available car inspection lane. About 30% of the incoming vehicles are trucks and the remaining are cars. Average inspection time for a truck is 5 min and average inspection time for a car is 6 min.
Also, authorities have noticed that about 50% of the trucks and 25% of the incoming cars need further scrutiny of contents and documents. For this, they are diverted to a separate lane in the Santa Barbara side of the border, where it takes about 8 min per vehicle to get checked thoroughly. This single "close scrutiny" lane is designed to handle both cars and trucks.
2. Suppose inspection times at all stages are distributed exponentially. On average, how long (in minutes) does each of the following vehicles take to go through from Tijuana to Santa Barbara at this border station?
a.. Normal Car:
b. Normal Truck:
c. Closely scrutinized Car:
d. Closely scrutinized Truck:
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