6OQ(d)

Expert-verifiedFound in: Page 345

Book edition
14th

Author(s)
F. Robert Jacobs

Pages
800 pages

ISBN
9780078024023

**Question: Students arrive at the Administrative Services Office at an average of one every 15 minutes, and their requests take on average 10 minutes to be processed. The service counter is staffed by only one clerk, Judy Gumshoes, who works eight hours per day. Assume Poisson arrivals and exponential service times.**

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**d. What are the probability that an arriving student (just before entering the Administrative Services Office) will me and at least one other student waiting in line?**

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**Answer**

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**Probability** is when a few clients ask for benefits at roughly the same time. This surge of clients incidentally over-burdens the benefits framework, creating a tube.

Holding up line models that survey benefit frameworks' execution ordinarily expect customers to arrive concurring to Poisson likelihood dissemination, and an exponential conveyance describes benefit times. The Poisson transportation indicates that many clients will come at a given time (per hour). The exponential passage portrays the benefit times as the probability that a specific benefit time will be less than or break even with a given time.

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**Step 1: Probability formula **

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The required probability is calculated using the following formula:

**Step 2: Probability that an arriving student (just before entering the Administrative Services Office) **

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The probability of at least one student standing in the line when another student arrives (which means there are total 2 students in the system) is

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