Answer:
At least 3 processing booths should be open.
Step-by-step explanation:
1 vehicle spends an average of 15 seconds in a booth
In N booths , there will be N/15 vehicles in 1 second
In 1 hr, there will be N/15 * 3600 vehicles
Therefore, there will be a total of 240N vehicles/hour
Actual arrival rate of vehicles at the airport is 500 veh/h
Probability of arrival, P =
P = 500/240N
P = 2.083/N
For the average time spends to be below 5 seconds
, since 500 is the average value.
Solving for N using the quadratic formula with a = 1, b = -2.0832, c = -0.0017
N = 1.0416 ± 1.0424
N = 2.084 or -0.0008
N = 2.084 is the only realistic value here
Therefore, the smallest number of processing booths that must be open should be 3