A distribution of service times at a waiting line shows that service takes 6 minutes 30% of the time, 7 minutes 40% of the time, 8 minutes 20% of the time, and 9 minutes 10% of the time. This distribution has been prepared for Monte Carlo analysis. The first two random numbers drawn are 53 and 74. The simulated service times are ________ minutes, then ________ minutes.
A) 6; 7
B) 7; 7
C) 7; 8
D) 8; 9
E) Cannot determine, because no service time probability is that large.

Question

Quizplus · Accepted Answer

To determine the simulated service time, we need to use the cumulative probabilities of the service times. We can create a table to calculate the cumulative probabilities:

Service Time | Probability | Cumulative Probability  
6 minutes   | 0.30       | 0.30  
7 minutes   | 0.40       | 0.70  
8 minutes   | 0.20       | 0.90  
9 minutes   | 0.10       | 1.00

Using the first random number, 53, we find the corresponding service time by comparing it to the cumulative probabilities in the table. 53 falls between the cumulative probabilities of 0.30 and 0.70, so the service time is in the range of 7 minutes to 8 minutes.

Using the second random number, 74, we find the corresponding service time by comparing it to the cumulative probabilities in the table. 74 falls between the cumulative probabilities of 0.70 and 0.90, so the service time is 8 minutes.

Therefore, the simulated service times are 7 minutes and 8 minutes. The answer is C.

A Distribution of Service Times at a Waiting Line Shows