Calculating customer inter-arrival time

Problem 1

During dinner hour, distribution of inter-arrival time of customers at Burger Barn is computed as follows:

Inter-arrival Time      Probability

30 seconds                 .45
60 seconds                 .25
90 seconds                 .15
120 seconds                .10
150 seconds                .05

Sixty percent of customers pay with cash, while 40% pay with credit cards.

Payment Method        Probability

Cash                             .60
Credit                            .40

Service time of the cash and credit card customers are estimated to be as follows:

             Cash                                          Credit Card

Service Time     Probability         Service Time        Probability

20 seconds           .35               30 seconds               .20
40 seconds           .30               60 seconds               .45
60 seconds           .25               90 seconds               .25
80 seconds           .10             120 seconds               .10

Simulate this system for 20 customer arrivals and find out the average time a cash and credit card customer should wait in line before paying cashier. Use random numbers in table below to find out the customer inter-arrival time, whether customer pays with cash or credit, the service time.

You would be working with three probabilistic variables, inter-arrival time, payment method and the service time. Also utilze excel template attached when solving this problem.

Random Numbers         

Inter-arrival Time              Payment Method               Service Time

63                                          10                                  19
46                                          73                                  79
86                                          28                                  35               
0                                             51                                63     
56                                           91                                 54    
67                                          14                                  51             
59                                          64                                  93
 28                                         24                                  69
79                                           70                                 14
64                                           84                                 35
33                                           73                                  1
81                                           17                                  9
17                                           48                                  70
63                                           11                                  50
66                                           88                                  40
27                                            94                                 41
4                                              29                                 71
34                                            83                                 68
7                                               71                                 50
69                                             27                                 82