A large insurance company maintains a central computing system that contains a variety of information about customer accounts. Insurance agents in a six-state area use telephone lines to access the customer information database. Currently, the company's central computer system allows three users to access the central computer simultaneously. Agents who attempt to use the system when it is full are denied access; no waiting is allowed. Management realizes that with its expanding business, more requests will be made to the central information system. Being denied access to the system is inefficient as well as annoying for agents. Access requests follow a Poisson probability distribution, with mean of 33 calls per hour. The service rate per line is 22 calls per hour. (a) What is the probability that 0, 1, 2, and 3 access lines will be in use? (Round your answers to four decimal places.) P(0) = 0.2388 P(1) 0.3582 P(2) = 0.2687 P(3)= 0.1343 (b) What is the probability that an agent will be denied access to the system? (Round your answers to four decimal places.) P=0.1343 (c) What is the average number of access lines in use? (Round your answers to two decimal places.) 1.73 X (d) In planning for the future, management wants to be able to handle λ = 43 calls per hour. In addition, the probability that an agent will be denied access to the system should be no greater than the value computed in part (b). How many access lines should this system have?
A large insurance company maintains a central computing system that contains a variety of information about customer accounts. Insurance agents in a six-state area use telephone lines to access the customer information database. Currently, the company's central computer system allows three users to access the central computer simultaneously. Agents who attempt to use the system when it is full are denied access; no waiting is allowed. Management realizes that with its expanding business, more requests will be made to the central information system. Being denied access to the system is inefficient as well as annoying for agents. Access requests follow a Poisson probability distribution, with mean of 33 calls per hour. The service rate per line is 22 calls per hour. (a) What is the probability that 0, 1, 2, and 3 access lines will be in use? (Round your answers to four decimal places.) P(0) = 0.2388 P(1) 0.3582 P(2) = 0.2687 P(3)= 0.1343 (b) What is the probability that an agent will be denied access to the system? (Round your answers to four decimal places.) P=0.1343 (c) What is the average number of access lines in use? (Round your answers to two decimal places.) 1.73 X (d) In planning for the future, management wants to be able to handle λ = 43 calls per hour. In addition, the probability that an agent will be denied access to the system should be no greater than the value computed in part (b). How many access lines should this system have?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![A large insurance company maintains a central computing system that contains a variety of information about customer accounts. Insurance agents in a six-state area use telephone lines to access the customer information database. Currently, the company's central computer system allows three users to access the central computer simultaneously. Agents who attempt to use the system when it is full are denied access; no waiting is allowed.
Management realizes that with its expanding business, more requests will be made to the central information system. Being denied access to the system is inefficient as well as annoying for agents. Access requests follow a Poisson probability distribution, with a mean of 33 calls per hour. The service rate per line is 22 calls per hour.
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**(a)** What is the probability that 0, 1, 2, and 3 access lines will be in use? (Round your answers to four decimal places.)
- \( P(0) = 0.2388 \)
- \( P(1) = 0.3582 \)
- \( P(2) = 0.2687 \)
- \( P(3) = 0.1343 \)
**(b)** What is the probability that an agent will be denied access to the system? (Round your answers to four decimal places.)
- \( P_k = 0.1343 \)
**(c)** What is the average number of access lines in use? (Round your answers to two decimal places.)
- 1.73
**(d)** In planning for the future, management wants to be able to handle \( \lambda = 43 \) calls per hour. In addition, the probability that an agent will be denied access to the system should be no greater than the value computed in part (b). How many access lines should this system have?
- [Answer box for calculation]
(Note: Ensure values and details are verified before implementation or use in decision-making.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe2fdea76-24b5-4e92-ab93-0d275ab88ec3%2Fd7ca63cc-6229-4463-b9fd-688afd61cd4e%2Fyiigja_processed.png&w=3840&q=75)
Transcribed Image Text:A large insurance company maintains a central computing system that contains a variety of information about customer accounts. Insurance agents in a six-state area use telephone lines to access the customer information database. Currently, the company's central computer system allows three users to access the central computer simultaneously. Agents who attempt to use the system when it is full are denied access; no waiting is allowed.
Management realizes that with its expanding business, more requests will be made to the central information system. Being denied access to the system is inefficient as well as annoying for agents. Access requests follow a Poisson probability distribution, with a mean of 33 calls per hour. The service rate per line is 22 calls per hour.
---
**(a)** What is the probability that 0, 1, 2, and 3 access lines will be in use? (Round your answers to four decimal places.)
- \( P(0) = 0.2388 \)
- \( P(1) = 0.3582 \)
- \( P(2) = 0.2687 \)
- \( P(3) = 0.1343 \)
**(b)** What is the probability that an agent will be denied access to the system? (Round your answers to four decimal places.)
- \( P_k = 0.1343 \)
**(c)** What is the average number of access lines in use? (Round your answers to two decimal places.)
- 1.73
**(d)** In planning for the future, management wants to be able to handle \( \lambda = 43 \) calls per hour. In addition, the probability that an agent will be denied access to the system should be no greater than the value computed in part (b). How many access lines should this system have?
- [Answer box for calculation]
(Note: Ensure values and details are verified before implementation or use in decision-making.)
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