In: Statistics and Probability
Show me how it is done in Excel if possible:
A store has one counter. The probability of inter-arrival time (in min) and service time (in min.) of customers are given in the following table.
Distribution of time between Arrival
Interarrival time(min) |
Probability |
Cumulative Probability |
Random Digit Assignment |
1 |
0.13 |
||
2 |
0.15 |
||
3 |
0.03 |
||
4 |
0.17 |
||
5 |
0.06 |
||
6 |
0.14 |
||
7 |
0.15 |
||
8 |
0.09 |
||
9 |
0.19 |
||
10 |
0.08 |
Distribution of Service-Time
Service Time(min) |
Probability |
Cumulative Probability |
Random Digit Assignment |
1 |
0.05 |
||
2 |
0.10 |
||
3 |
0.20 |
||
4 |
0.30 |
||
5 |
0.25 |
||
6 |
0.10 |
The table for interarrival time is as follows
THe cumulative Probability is obtained by just summing the Proababilities till that value
For example cumulative probability of Interval time 2 mins = 0.13 + 0.15 = 0.28
For example cumulative probability of Interval time 3 mins = 0.13 + 0.15 + 0.03 = 0.31
Likewise the other values are calculated and shown in the above image
For random digit assignment, the steps are as follows
Step 1 : In the cell G5, type the formula =RAND()
Step 2 : Drag the formula from G5 to G14. Now we will have random decimal numbers in cells G5 to G14
Step 3: Now go to Cell F5. Type the formula =RANK.EQ(G5,$G$5:$G$14)
Step 2 : Drag the formula from F5 to F14. Now we will have random digits assigned in cells F5 to F14
We combine the RAND() and RANK.EQ() formulas to ge tthe random digits
The table for service time is as follows
The cumulative Probability is obtained by just summing the Proababilities till that value
For example cumulative probability of service time 2 mins = 0.05 + 0.1 = 0.15
For example cumulative probability of Interval time 3 mins = 0.05 + 0.1 + 0.2 = 0.35
Likewise the other values are calculated and shown in the above image
For random digit assignment, the steps are as follows
Step 1 : In the cell G5, type the formula =RAND()
Step 2 : Drag the formula from G5 to G10. Now we will have random decimal numbers in cells G5 to G10
Step 3: Now go to Cell F5. Type the formula =RANK.EQ(G5,$G$5:$G$10)
Step 2 : Drag the formula from F5 to F10. Now we will have random digits assigned in cells F5 to F10
We combine the RAND() and RANK.EQ() formulas to ge tthe random digits