Question

A dry cleaning shop has a drive-through window for fast service. The following tables provide information about the time between arrivals and the service times required at the window on a particularly busy day of the week. Time Between Arrivals (minutes) Probability 7 0.1 8 0.3 9 0.4 10 0.2 Service Time (hours) Probability 3 0.1 5 0.2 12 0.2 24 0.5 If the store opens at 8:00 a.m., and random numbers are used to generate arrivals, what time would the fifth customer arrive if the random numbers were 02, 33, 81, 24, 03 and how long would the service take if the random number for the fifth customer was 77? a. Arrival time 8:34; service time 5 hours b. Arrival time 8:36; service time 5 hours c. Arrival time 8:40; service time 24 hours d. Arrival time 8:24, service time 12 hours.

Answer 1

Answer to Question:

From the Simulated Data Table, we can conclude that the 5th customer would arrive at 8.40 A.M  and it would take 24 hours to serve the 5th customer.

c) Arrive time 8.40 ; Service time 24 hours

Random Number Allocation Table

Time between arrival
Minutes	Probability	Cum. Probability	Range
7	0.1	0.1	0-9
8	0.3	0.4	10-39
9	0.4	0.8	40-79
10	0.2	1	80-99
Service Time
Hours	Probability	Cum. Probability	Range
3	0.1	0.1	0-9
5	0.2	0.3	10-29
12	0.2	0.5	30-49
24	0.5	1	50-99

Statement of Simulated Data:

Serial No	Random No.	Arrival time (in mins)	Arrival Time A.M	Service Begins A.M	Random No.	Service time (hours)
1	2	7	8.07	8.03
2	33	8	8.15
3	81	10	8.25
4	24	8	8.33
5	3	7	8.40		77	24