Answer:
option (b) Approximately 98 minutes
Explanation:
Given:
Average arrival rate, λ = 6 per 8 hour or [tex]\frac{\textup{6}}{\textup{8}\times60}[/tex] = 0.0125 / minute
Service Rate, μ = [tex]\frac{\textup{1}}{\textup{50}}[/tex] = 0.02/min
Standard Deviation = 20 minutes
Now,.
Utilization Rate, ρ = [tex]\frac{\lambda}{\mu}[/tex]
or
= [tex]\frac{\textup{0.0125}}{0.02}[/tex]
= 0.625
and,
Number of people in Queue = [tex]\frac{\lambda^2\times\sigma^2+\rho^2}{2\times(1-\rho)}[/tex]
or
= [tex]\frac{0.0125^2\times20^2+0.625^2}{2\times(1-0.625)}[/tex]
= 0.6042
and,
Waiting in the Queue = [tex]\frac{\textup{Number of people in Queue}}{\lambda}[/tex]
= [tex]\frac{\textup{0.6042}}{0.0125}[/tex]
= 48.33 minutes
Thus,
Waiting Time in Office = Wait in the Queue + [tex]\frac{\textup{1}}{\textup{Service rate}}[/tex]
= 48.33 minutes + [tex]\frac{\textup{1}}{\textup{0.02}}[/tex]
= 48.33 + 50
= 98.33 minutes
hence, the answer is option (b) Approximately 98 minutes