Question

QUESTION 1

1. Use the following scenario and data for all questions
   An auto service center provides two types of services, Tire Replacement (T) and Oil Change (O). About 30% of the customers are for Tire Replacement and the other 70% are for Oil Change. All customers are serviced on a first come first served basis. During regular hours, customers arrive at the service center according to the probability distribution in the following table
   
   Two technicians are working at the service center and both of them are skillful enough for both Tire Replacement and Oil Change. Once finishing the job for a customer, a technician will take care of the next customer waiting in line. When both technicians are idle, the one who finished the last job earlier will take care of the next incoming customer. The times taken by the two jobs by any of the technicians follow the probability distributions in the following tables. You are required to simulate the operations of the auto service center for 15 customers.
   
   Before answering the following questions, you may use the following tables to determine the cumulative probability distributions and assign random number intervals for customer arrivals, customer service types, and time needed for both types of services.
   
   
   You may also simulate the operations of this auto service center for the 15 customers using the random numbers given in the following table. The “Start Time” is the time point when the job for the customer starts and the “Finish Time" is the time point when the job for the customer finishes.
   
   
   
   
   For customer arrivals, the random number interval assigned to the Time between Arrivals of 5 minutes is

   		0.0000-0.1499
   		0.1500-0.3999
   		0.4000-0.7999
   		0.8000-0.9999
   		None of the above

1 points   

QUESTION 2

1. For customer arrivals, the random number interval assigned to the Time between Arrivals of 15 minutes is

   		0.0000-0.1499
   		0.1500-0.3999
   		0.4000-0.7999
   		0.8000-0.9999
   		None of the above

1 points   

QUESTION 3

1. For the Customer Service Type, the random number interval assigned to Tire Replacement is

   		0.0000-0.6999
   		0.0000-0.2999
   		0.2999-0.9999
   		0.3000-0.9999
   		None of the above

1 points   

QUESTION 4

1. For the Customer Service Type, the random number interval assigned to Oil Change is

   		0.0000-0.6999
   		0.0000-0.2999
   		0.2999-0.9999
   		0.3000-0.9999
   		None of the above

1 points   

QUESTION 5

1. For the Tire Replacement, the random number interval assigned to Service Time 25 minutes is

   		0.0000-0.1999
   		0.2000-0.4499
   		0.4500-0.8499
   		0.8500-0.9999
   		None of the above

1 points   

QUESTION 6

1. For the Tire Replacement, the random number interval assigned to Service Time 35 minutes is

   		0.0000-0.1999
   		0.2000-0.4499
   		0.4500-0.8499
   		0.8500-0.9999
   		None of the above

1 points   

QUESTION 7

1. For the Oil Change, the random number interval assigned to the Service Time 15 minutes is

   		0.0000-0.2999
   		0.3000-0.6999
   		0.7000-0.8999
   		0.9000-0.9999
   		None of the above

Answer 1

From the information

Customer arrival :

Time between arrivals	Probability	Cumultive Probability	Random number interval
1	0.05	0.05	0.0000-0.0499
2	0.15	0.2	0.0500-0.1999
3	0.2	0.4	0.2000-0.3999
4	0.4	0.8	0.4000-0.7999
5	0.2	1	0.8000-0.9999

From the table

The random number interval assigned for the time between arrival of 2 minutes is 0.0500-0.1999.

Correct answer: 0.0500-0.1999.

From the table

The random number interval assigned for the time between arrival of 5 minutes is 0.8000-0.9999.

Correct answer: 0.8000-0.9999

Pump 1: (Self service).

Service Time (in minutes)	Probability	Cumulative Probability	Random number interval
4	0.15	0.15	0.0000-0.1499
5	0.25	0.4	0.1500-0.3999
6	0.4	0.8	0.4000-0.7999
7	0.2	1	0.8000-0.9999

From the above table the for self service pump random number interval assigned to service time of 4 minutes is 0.0000-0.1499

Correct answer : 0.0000-0.1499

From the above table the for self service pump random number interval assigned to service time of 6 minutes is 0.4000-0.7999

Correct answer :0.4000-0.7999.

Pump 2: (full service).

Service Time (in minutes)	Probability	Cumulative Probability	Random number interval
5	0.20	0.20	0.0000-0.1999
6	0.30	0.50	0.2000-0.4999
7	0.40	0.90	0.5000-0.8999
8	0.10	1	0.9000-0.9999

From the above table the for full service pump random number interval assigned to service time of 5 minutes is 0.0000-0.1999

Correct answer : 0.0000-0.1999

From the above table the for full service pump random number interval assigned to service time of 8 minutes is 0.9000-0.9999

Correct answer : 0.9000-0.9999​​​​​​​.