Answer:
the average number of students waiting in line to be served = 0.640 = 16/25 arrivals/min
Step-by-step explanation:
Explanation:-
Students arrive at the Daz Bog counter to buy frou-frou coffee drinks (with whipped cream) on average every 12 minutes so its means the arrival rate
λ = 1/12minutes
Given an average time of 6.5 minutes to serve each customer, with service times following an Exponential distribution
so given the service rate μ= 1/6.5 per min
The formula of the average number of students waiting in line to be served
that is Average length of the queue
[tex]L_{q} = \frac{λ^2}{μ (μ -λ)}[/tex]
[tex]L_{q} = \frac{(\frac{1}{12} )^2}{\frac{1}{6.5} (\frac{1}{6.5} -\frac{1}{12} )}[/tex]
on simplification , we get
[tex]L_{q} = 0.640 = \frac{640}{1000} = \frac{16}{25}[/tex] arrivals/min
