A distribution of service times at a waiting line indicates that service takes 12 minutes 30 percent of the time and 14 minutes 70 percent of the time. This distribution has been prepared for Monte Carlo analysis. The first four random numbers drawn are 07, 60, 77, and 49. What is the average service time of this simulation?
A) 12 minutes
B) 13 minutes
C) 13.5 minutes
D) 14 minutes
E) 54 minutes

Question

Quizplus · Accepted Answer

To use Monte Carlo analysis, we need to randomly select values from the distribution of service times. The given percentage frequencies tell us that 30% of the time, the service time is 12 minutes, and 70% of the time it is 14 minutes. We can use the random numbers drawn to simulate this process. 
If a random number falls between 0 and 30, we take the service time to be 12 minutes. If the random number falls between 31 and 100, we take the service time to be 14 minutes. 
For the first four random numbers drawn (07, 60, 77, and 49), we get a service time of 12, 14, 14, and 14 minutes, respectively. 
The average service time for these four simulations is (12 + 14 + 14 + 14)/4 = 13.5 minutes, which is the answer to the question.

A Distribution of Service Times at a Waiting Line Indicates