Question

In: Statistics and Probability

Problem 11-30 (Algorithmic) A large insurance company maintains a central computing system that contains a variety...

Problem 11-30 (Algorithmic)

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 34 calls per hour. The service rate per line is 12 calls per hour.

  1. What is the probability that 0, 1, 2, and 3 access lines will be in use? Round your answers to 4 decimal places.
    j Pj
    0
    1
    2
    3
  2. What is the probability that an agent will be denied access to the system? Round your answers to 4 decimal places.

  3. What is the average number of access lines in use? Round your answers to 4 decimal places.

    L =
  4. In planning for the future, management wants to be able to handle λ = 42 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? (already calculated 5 to be the answer)

This is all one question.

Solutions

Expert Solution


Related Solutions

Problem 11-30 (Algorithmic) A large insurance company maintains a central computing system that contains a variety...
Problem 11-30 (Algorithmic) 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...
Problem 11-30 (Algorithmic) A large insurance company maintains a central computing system that contains a variety...
Problem 11-30 (Algorithmic) 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...
A large insurance company maintains a central computing system that contains a variety of information about...
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...
A large insurance company maintains a central computing system that contains a variety of information about...
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...
A large insurance company maintains a central computing system that contains a variety of information about...
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 Limit Theorem) An insurance company serves 10 large customers. The insurance claim placed by each...
(Central Limit Theorem) An insurance company serves 10 large customers. The insurance claim placed by each customer in a year is uniformly distributed between 0 and 100. Assume that the insurance claims from different customers are independent. Use the central limit theorem to approximately compute the probability that the total insurance claim placed by all customers in a year exceeds 625. Let Φ(x) denote the cumulative distribution function of a standard normal distribution, i.e. a normal distribution with mean 0...
Problem 16-11 (Algorithmic) In preparing for the upcoming holiday season, Fresh Toy Company (FTC) designed a...
Problem 16-11 (Algorithmic) In preparing for the upcoming holiday season, Fresh Toy Company (FTC) designed a new doll called The Dougie that teaches children how to dance. The fixed cost to produce the doll is $100,000. The variable cost, which includes material, labor, and shipping costs, is $34 per doll. During the holiday selling season, FTC will sell the dolls for $42 each. If FTC overproduces the dolls, the excess dolls will be sold in January through a distributor who...
Problem 16-11 (Algorithmic) In preparing for the upcoming holiday season, Fresh Toy Company (FTC) designed a...
Problem 16-11 (Algorithmic) In preparing for the upcoming holiday season, Fresh Toy Company (FTC) designed a new doll called The Dougie that teaches children how to dance. The fixed cost to produce the doll is $100,000. The variable cost, which includes material, labor, and shipping costs, is $34 per doll. During the holiday selling season, FTC will sell the dolls for $42 each. If FTC overproduces the dolls, the excess dolls will be sold in January through a distributor who...
Problem 16-11 (Algorithmic) In preparing for the upcoming holiday season, Fresh Toy Company (FTC) designed a...
Problem 16-11 (Algorithmic) In preparing for the upcoming holiday season, Fresh Toy Company (FTC) designed a new doll called The Dougie that teaches children how to dance. The fixed cost to produce the doll is $100,000. The variable cost, which includes material, labor, and shipping costs, is $34 per doll. During the holiday selling season, FTC will sell the dolls for $42 each. If FTC overproduces the dolls, the excess dolls will be sold in January through a distributor who...
Problem 16-11 (Algorithmic) In preparing for the upcoming holiday season, Fresh Toy Company (FTC) designed a...
Problem 16-11 (Algorithmic) In preparing for the upcoming holiday season, Fresh Toy Company (FTC) designed a new doll called The Dougie that teaches children how to dance. The fixed cost to produce the doll is $100,000. The variable cost, which includes material, labor, and shipping costs, is $34 per doll. During the holiday selling season, FTC will sell the dolls for $42 each. If FTC overproduces the dolls, the excess dolls will be sold in January through a distributor who...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT