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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

## Answer

**Course:** Basic Statistics

**Ref. No:-** TGS01841