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 37 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) 0.1642 X P(1) = 0.2911 X P(2) = 0.2572 X P(3) = 0.1521 x (b) What is the probability that an agent will be denied access to the system? (Round your answers to four decimal places.) P = 0.1521 X (c) What is the average number of access lines in use? (Round your answers to two decimal places.) 0.56 X
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 37 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) 0.1642 X P(1) = 0.2911 X P(2) = 0.2572 X P(3) = 0.1521 x (b) What is the probability that an agent will be denied access to the system? (Round your answers to four decimal places.) P = 0.1521 X (c) What is the average number of access lines in use? (Round your answers to two decimal places.) 0.56 X
Chapter9: Sequences, Probability And Counting Theory
Section9.5: Counting Principles
Problem 52SE: A car wash offers the following optional services to the basic wash: clear coat wax, triple foam...
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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 37 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) = 0.1642
P(1) = 0.2911
P(2) = 0.2572
P(3) = 0.1521
X
X
X
X
(b) What is the probability that an agent will be denied access to the system? (Round your answers to four decimal places.)
P = 0.1521
k
X
(c) What is the average number of access lines in use? (Round your answers to two decimal places.)
0.56
X
(d) In planning for the future, management wants to be able to handle
45 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?
4
=
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