With an average service rate of 15 customers per hour and an average customer arrival rate of 12 customers per hour, calculate the probability that actual service time will be less than or equal to five minutes.

Question

Georgina

Mathematics

28 October, 13:47

With an average service rate of 15 customers per hour and an average customer arrival rate of 12 customers per hour, calculate the probability that actual service time will be less than or equal to five minutes.

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Holly Hanson · Answer 1

probability that actual service time will be less than or equal to five minutes = P (X < = 5) = 1 - e-15 (5/60) = 0.714 or 71.4%

Step-by-step explanation:

The identification of the average arrival rate of customers (v) and the average service rate (u) must be done in order to solve this kind of problem.

In this case, on average, 12 customers arrive each hour. On average, the service rate is 15 customers per hour.

The arrival rate follows the exponential distribution.

probability that actual service time will be less than or equal to 't' minutes P (X < = t) = 1 - e-u (t/60)

probability that actual service time will be less than or equal to five minutes = P (X < = 5) = 1 - e-15 (5/60) = 0.714 or 71.4%