A distribution of service times at a waiting line indicates that service takes 6 minutes 30 percent of the time,7 minutes 40 percent of the time,8 minutes 20 percent of the time,and 9 minutes 10 percent of the time.In preparing this distribution for Monte Carlo analysis,the service time of 8 minutes would be represented by what random number range?
A)20 through 40
B)21 through 40
C)70 through 90
D)71 through 90
E)01 through 20

Question

Quizplus · Accepted Answer

To represent the service time of 8 minutes, we need to find the cumulative percentage up to 8 minutes.

Cumulative Percentage up to 8 minutes: 
= Percentage of service time for 6 minutes + Percentage of service time for 7 minutes + Percentage of service time for 8 minutes
= 30% + 40% + 20%
= 90%

This means that 90% of the time, service time is less than or equal to 8 minutes. To represent this in a random number range, we need to find the equivalent range of numbers that covers 90% of the total range (0-99).

0-99 range covers 100% of the time, so 90% of the range would be: 
= 0-89

But since we start counting from 1 in Monte Carlo analysis, the range would be:
= 1-90

To cover the remaining 10% of the time, we can assign the range of 91-100 to represent the service time of 9 minutes.

Therefore, the random number range to represent the service time of 8 minutes is 71 through 90.

A Distribution of Service Times at a Waiting Line Indicates