Answer:
Step-by-step explanation:
Given
Expected no of customer in the system is 4 i.e. length of queue is [tex]L=4[/tex]
Expected waiting time in the system [tex]W=80\ min[/tex]
Length of queue is given by
[tex]L=\frac{\rho }{1-\rho }[/tex]
[tex]4=\frac{\rho }{1-\rho }[/tex]
thus [tex]\rho =\frac{4}{5}[/tex]
where [tex]\rho =\frac{mean\ arrival\ rate}{mean\ service\ rate}[/tex]
L is also given by
[tex]L=\lambda \times W[/tex]
therefore
[tex]\lambda =\frac{4}{80}=\frac{1}{20}[/tex]
where [tex]\lambda [/tex]=mean arrival rate
[tex]\mu [/tex]=mean service rate
Probability that customer service rate is less than 40 minutes is
[tex]P=1-\rho e^{-\mu (1-\rho )\cdot t}[/tex]
[tex]P=1-0.8\times e^{-\frac{1}{16}\times 0.2\times 40}[/tex]
[tex]P=1-0.4852[/tex]
[tex]P=0.5147[/tex]
