Question

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

Answer 1

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