The number of customers approaching the tailor appears to be Pois
| The number of customers approaching the tailor appears to be Poisson distributed with a mean of 6 customers per hour. The tailor attends the customers on a first-come-first-serve basis and the customers wait if they need to. The tailor can attend the customers at an average rate of 10 customers per hour with the service time exponentially distributed. The probability that the system is idle is ____
A. 0.7
B. 0.3
C. 0.6
D. 0.4
Please scroll down to see the correct answer and solution guide.
Right Answer is: D
SOLUTION
Concept:
Probability that system is idle is given by:
\({P_0} = 1 - \frac{\lambda }{\mu }\)
where, λ = arrival rate and μ = service rate
Calculation:
Given:
λ = 6 customers per hour, μ = 10 customers per hour
Now,
Probability that system is idle,
\({P_0} = 1 - \frac{\lambda }{\mu }\)
\({P_0} = 1 - \frac{6}{{10}}\)
∴ P0 = 0.4