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Answer :
The length of the line is approximately 5 people.
To find the length of the line given the arrival rate, service rate, and average waiting time, you can use the following formula:
Length of the line = (Arrival rate × Average waiting time) + (Arrival rate / Service rate)
First, convert the average waiting time from minutes to hours:
24 minutes = 24/60 = 0.4 hours
Now, plug in the given values into the formula:
Length of the line = (9 arrivals/hour × 0.4 hours) + (9 arrivals/hour / 14 services/hour)
Length of the line = (3.6 arrivals) + (0.6429 arrivals)
Length of the line ≈ 4.24 arrivals
Since you can't have a fraction of a person in the line, round up to the nearest whole number:
Length of the line ≈ 5 arrivals
So, the length of the line is approximately 5 people.
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