Answer :
The probability that there are no more than 3 cars in the system is 0.50
Probability:
In math, the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes is referred as probability.
Given,
Because of limited space availability and a desire to provide an acceptable level of service, the bank manager would like to have no more than three cars in the system at any time.
Here we need to find the probability that there are no more than 3 cars in the system.
Here we know that the present level of service for three or fewer cars is the probability that there are 0, 1, 2, or 3 cars in the system.
As per the Model 1, Exhibit 8A.8, the probability of having more than three cars in the system is 1.0 minus the probability of three or fewer cars => 1.0 − 0.685 = 31.5 percent
And the 95 percent service level of three or fewer cars, this states that
=> P0 + P1 + P2 + P3 = 95 percent.
When we can solve this by trial and error for values of λ/μ.
Therefore, the value of λ/μ = 0.50
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