Final answer:
Using Little's Law, with an entry rate of 72 people per minute and an average of 3,200 people in the system, a person spends an average of 44.444 minutes in the airport security checkpoint.
Step-by-step explanation:
The student is asking how long, on average, a person spends in an airport security checkpoint given the rate at which people enter the checkpoint and the average number of people in the checkpoint at any time.
Using Little's Law, we can calculate this by dividing the average number of people in the system (L) by the rate at which they enter (λ). The formula for Little's Law is L = λW, where W is the average time a person spends in the system. We can rearrange the formula to solve for W, which is W = L/λ.
Given that L is 3,200 people and λ is 72 people per minute, we calculate W as follows:
W = 3,200 people / 72 people/minute = 44.444 minutes. Therefore, on average, a person spends 44.444 minutes in the airport security checkpoint.