## Processing times for jobs are normally distributed, with mean 50 minutes and standard deviation 8 minutes

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Processing times for jobs are normally distributed, with mean 50 minutes and standard deviation 8 minutes. Construct a simulation table and perform a simulation for 10 new customers. Assume that, when the simulation begins, there is one job being processed (scheduled to be completed in 25 minutes) and there is one job with a 50-minute processing time in the queue.

 Time Between Arrivals (Hours) Probability 0 .23 1 .37 2 .28 3 .12

a) what was the avg. time in the queue for the 10 new jobs?

b) what was the avg. processing time of the 10 new jobs?

c) what was the max. time in the system for the 10 new jobs?

Question 1: How does the fact that the jobs are normally distributed impact the solution?

Question 2: Can you kindly solve it in Excel?

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8 months 2023-01-28T17:43:39+00:00 2 Answers 79 views Teacher 0

1. ### Please briefly explain why you feel this answer should be reported .

Question 1: The fact that the jobs are normally distributed impacts the solution because normal distribution is a useful tool in modeling job processing times. It allows us to calculate the probability of a job being completed in a certain amount of time and provides a mean and standard deviation to understand the variability in processing times.

Question 2:

a) To calculate the average time in the queue for the 10 new jobs, we need to keep track of the total waiting time for all 10 jobs and then divide that by 10. We can use a random number generator in Excel to generate random arrival times for the 10 new customers, and then calculate the waiting time for each customer based on when the previous job was completed.

b) To calculate the average processing time of the 10 new jobs, we can use a random number generator in Excel to generate random processing times for each of the 10 jobs based on the mean and standard deviation. Then, we can calculate the average processing time by summing all the processing times and dividing by 10.

c) To calculate the maximum time in the system for the 10 new jobs, we can calculate the sum of the waiting time and processing time for each job and then find the maximum value.

2. ### Please briefly explain why you feel this answer should be reported .

To simulate the queue, we can generate random numbers for the time between arrivals using the given probabilities and the RAND() function in Excel. We can then use the random numbers to calculate the arrival times of the 10 new customers. For the processing times, we can generate random numbers from a normal distribution with a mean of 50 minutes and a standard deviation of 8 minutes using the NORM.INV() function in Excel.

a) To calculate the average time in the queue for the 10 new jobs, we need to simulate the arrival times and processing times for each job, and then calculate the time spent in the queue for each job. We can use the following simulation table:

CustomerTime Between ArrivalsArrival TimeProcessing TimeStart TimeFinish TimeTime in Queue
1=IF(RAND()<0.23,0,IF(RAND()<0.37,1,IF(RAND()<0.28,2,3)))=B2+D2=NORM.INV(RAND(),50,8)=MAX(C2,E1)=F2+D2=D2-E2
2=IF(RAND()<0.23,0,IF(RAND()<0.37,1,IF(RAND()<0.28,2,3)))=B3+D3=NORM.INV(RAND(),50,8)=MAX(C3,E2)=F3+D3=D3-E3
3=IF(RAND()<0.23,0,IF(RAND()<0.37,1,IF(RAND()<0.28,2,3)))=B4+D4=NORM.INV(RAND(),50,8)=MAX(C4,E3)=F4+D4=D4-E4
4=IF(RAND()<0.23,0,IF(RAND()<0.37,1,IF(RAND()<0.28,2,3)))=B5+D5=NORM.INV(RAND(),50,8)=MAX(C5,E4)=F5+D5=D5-E5
5=IF(RAND()<0.23,0,IF(RAND()<0.37,1,IF(RAND()<0.28,2,3)))=B6+D6=NORM.INV(RAND(),50,8)=MAX(C6,E5)=F6+D6=D6-E6
6=IF(RAND()<0.23,0,IF(RAND()<0.37,1,IF(RAND()<0.28,2,3)))=B7+D7=NORM.INV(RAND(),50,8)=MAX(C7,E6)=F7+D7=D7-E7
7=IF(RAND()<0.23,0,IF(RAND()<0.37,1,IF(RAND()<0.28,2,3)))=B8+D8=NORM.INV(RAND(),50,8)=MAX(C8,E7)=F8+D8=D8-E8
8=IF(RAND()<0.23,0,IF(RAND()<0.37,1,IF(RAND