Question

The​ Solomon, Smith, and Samson law firm produces many legal documents that must be word processed for clients and the firm. Requests average pages of documents per​ hour, and they arrive according to a Poisson distribution. The secretary can word process pages per hour on average according to an exponential distribution.

a. The average utilization rate of the secretary is _________​% utilization. ​
b. The probability that more than four pages are waiting or being word processed is _____. (Enter your response rounded to three decimalplaces.)
c. The average number of pages waiting to be word processed is ____pages. (Enter your response rounded to two decimal places.)

Answer 1

Arrival rate λ= 19 pages per hour

Service rate μ = 20 pages per hour

a. Average utilization rate P = λ/μ

Average utilization rate P = 19/20

Average utilization rate P = 0.95

Average utilization rate P = 95%

b. Probability that more than four pages are waiting or being word processed Pn>4 = 1 - (P0 + P1 + P2 + P3 + P4)

Pn>4 = 1 - (0.05*(1+0.95 + 0.95^2 + 0.95^3 + 0.95^4))

Pn>4 = 1 - (0.05*4.524)

Pn>4 = 1 - 0.2262

Pn>4 = 0.774.

c. Average number of pages waiting to be word processed Lq

Lq = λ²/μ(μ-λ)

Lq = 19²/20(20-19)

Lq = 361/20

Lq = 18.05