The computer lab at State University has a help desk to assist students working on computer spreadsheet assignments. The students patiently form a single line in front of the desk to wait for help. Students are served based on a first-come, first-served priority rule. Students arrive at the help desk at the rate of 4 every 10 minutes. The average service time is 2 minutes. The Poisson distribution is appropriate for the arrival rate and service times are exponentially distributed. a) What is the average time a student is in the lab? b) What is the average number of students in the lab? c) What is the average number of students waiting to receive service?
The computer lab at State University has a help desk to assist students working on computer spreadsheet assignments. The students patiently form a single line in front of the desk to wait for help. Students are served based on a first-come, first-served priority rule. Students arrive at the help desk at the rate of 4 every 10 minutes. The average service time is 2 minutes. The Poisson distribution is appropriate for the arrival rate and service times are exponentially distributed. a) What is the average time a student is in the lab? b) What is the average number of students in the lab? c) What is the average number of students waiting to receive service?
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 26PPS
Related questions
Question
![The computer lab at State University has a help desk to assist students working on computer
spreadsheet assignments. The students patiently form a single line in front of the desk to wait for help.
Students are served based on a first-come, first-served priority rule. Students arrive at the help desk at
the rate of 4 every 10 minutes. The average service time is 2 minutes. The Poisson distribution is
appropriate for the arrival rate and service times are exponentially distributed.
a) What is the average time a student is in the lab?
b) What is the average number of students in the lab?
c) What is the average number of students waiting to receive service?
d) What is the average time a student is in the queue?
e) What is the probability that there are no students at the computer lab?
f) What percentage of the time is the help desk busy?
g) What is the probability that there are exactly 2 students in the lab?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd9d0674d-863d-4f0d-a871-dbf4fd48e1a5%2F55d4351e-61e7-4d26-9a19-38823cc86dca%2Fjn0lf7m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The computer lab at State University has a help desk to assist students working on computer
spreadsheet assignments. The students patiently form a single line in front of the desk to wait for help.
Students are served based on a first-come, first-served priority rule. Students arrive at the help desk at
the rate of 4 every 10 minutes. The average service time is 2 minutes. The Poisson distribution is
appropriate for the arrival rate and service times are exponentially distributed.
a) What is the average time a student is in the lab?
b) What is the average number of students in the lab?
c) What is the average number of students waiting to receive service?
d) What is the average time a student is in the queue?
e) What is the probability that there are no students at the computer lab?
f) What percentage of the time is the help desk busy?
g) What is the probability that there are exactly 2 students in the lab?
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Glencoe Algebra 1, Student Edition, 9780079039897…](https://www.bartleby.com/isbn_cover_images/9780079039897/9780079039897_smallCoverImage.jpg)
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
![Big Ideas Math A Bridge To Success Algebra 1: Stu…](https://www.bartleby.com/isbn_cover_images/9781680331141/9781680331141_smallCoverImage.jpg)
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
![Holt Mcdougal Larson Pre-algebra: Student Edition…](https://www.bartleby.com/isbn_cover_images/9780547587776/9780547587776_smallCoverImage.jpg)
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
![Glencoe Algebra 1, Student Edition, 9780079039897…](https://www.bartleby.com/isbn_cover_images/9780079039897/9780079039897_smallCoverImage.jpg)
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
![Big Ideas Math A Bridge To Success Algebra 1: Stu…](https://www.bartleby.com/isbn_cover_images/9781680331141/9781680331141_smallCoverImage.jpg)
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
![Holt Mcdougal Larson Pre-algebra: Student Edition…](https://www.bartleby.com/isbn_cover_images/9780547587776/9780547587776_smallCoverImage.jpg)
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL