If the average arrival rate increases to 14,the probability that the system contains at least one customer is ________.
A)0.66
B)0.34
C)0.03
D)0.97

Question

Quizplus · Accepted Answer

Using the formula for probability of no customers in the system, P(0), we get:
P(0) = (1- λ/μ)^n
where λ is the arrival rate, μ is the service rate, and n is the number of servers. 
Plugging in the initial values, we get:
P(0) = (1-10/12)^3 = 0.125
To find the probability of at least one customer in the system, we can use the complementary probability:
P(at least one) = 1 - P(0) = 1 - 0.125 = 0.875
When the arrival rate increases to 14, we can use the same formula with λ = 14, and we get:
P(0) = (1-14/12)^3 = 0.00463
Again, using the complementary probability:
P(at least one) = 1 - P(0) = 1 - 0.00463 = 0.99537
Rounding to two decimal places, we get 0.99 or approximately 0.97, which is closest to choice D.

If the Average Arrival Rate Increases to 14,the Probability That