Question

In: Statistics and Probability

An office employs several clerks who create documents, and one operator who enters the document information...

An office employs several clerks who create documents, and one operator who enters the document information in a computer system. The group creates documents at a rate of 14 per hour. The operator can enter the information with an average exponentially distributed time of 3 minutes. Assume the population is infinite, arrivals are Poisson, and queue length is infinite with the FCFS discipline.

a. Calculate the percentage utilization of the operator. (Round your answer to 2 decimal places.)

b. Calculate the average number of documents in the system. (Round your answer to 1 decimal place.)

c. Calculate the average time in the system. (Round your answer to 1 decimal place.)

d. Calculate the probability of four or more documents being in the system. (Round your intermediate calculations to 3 decimal places and final answer to 1 decimal place.

Expert Solution

Answer :

Given that :

No.of documents per hour = = 14

Let us take

Time t = 3

a)The percentage utilization of the operator is = P

= 14 / 21

= 0.6667

= 66.67%

b)The average number of documents in the system is =

= 14 / (21 - 14)

= 2

So,the documents in system = 2

c)The avg time in system =

= 2 / 21

= 0.0952 hrs

= 5.714 minutes

= 6 minutes

d)Probability of 4 or more documents = 0,1,2,3

0 = 66.67

1 = 66.67 * 66.67% = 44.45

2 = 44.45 * 66.67 % = 29.63

3 = 29.63 * 66.67 % = 19.75

Finally the probability of 4 or more documents = 19.75

orchestra answered 2 years ago

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