A fast-food company is developing a computer simu-lation involving arrival time at a drive-through restaurant. The distribution for arrival times is:
Time -
Single-Digit Random -
Between Arrivals -
Probability -
Number Assigned -
2 minutes
0.1
3 minutes
0.2
1, 2
4 minutes
0.3
3, 4, 5
5 minutes
0.4
6, 7, 8, 9
Six random numbers are selected to represent the arrival of six cars: 1, 6, 9, 0, 5, 6.
What is the mean time between arrivals in this run of the simu-lation model?
To determine the mean time between arrivals for the six cars, we need to look at the associated random numbers and their corresponding arrival times as given in the distribution. The random numbers are 1, 6, 9, 0, 5, and 6. According to the given distribution: 1 corresponds to 3 minutes, 6 corresponds to 5 minutes, 9 corresponds to 5 minutes, 0 corresponds to 5 minutes, 5 corresponds to 4 minutes, and 6 corresponds to 5 minutes. Adding these times together and then dividing by the number of cars (6) gives the mean time: (3 + 5 + 5 + 5 + 4 + 5) / 6 = 27 / 6 = 4.5 minutes. Therefore, the mean time between arrivals is 4 minutes.
Just an observation...I believe this question is associated with the topic covered in the 2nd CIA exam, which would address topics such as sampling methods.
I agree! This is not covered in part 1 syllabus
The cars selected randomly are cars 1; 6; 9; 0; 5 and 6. Their respective probabilities = 0,2 ; 0,4 ; 0,1 ; 0,3 ; and 0,4. Their respective arrival times = 3; 5; 5; 2; 4; 5. For the 6 cars, the mean time is 4 minutes = (3+5+5+2+4+5)/6