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borishaifa [10]
3 years ago
10

The​ Solomon, Smith, and Samson law firm produces many legal documents that must be word processed for clients and the firm. Req

uests 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.)
Business
1 answer:
stepan [7]3 years ago
4 0

Answer:

Arrival rate λ= 19 pages per hour

Service rate μ = 20 pages per hour

a.  Average utilization rate <em>P </em>=  λ/μ

Average utilization rate <em>P </em>= 19/20

Average utilization rate <em>P </em>= 0.95

Average utilization rate <em>P = </em> 95%

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

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 <em>Lq</em>

<em>Lq = </em>λ²/μ(μ-λ)

<em>Lq </em>= 19²/20(20-19)

<em>Lq </em>= 361/20

<em>Lq </em>= 18.05

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