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During tax season, the IRS hires seasonal workers to help answer the questions of taxpayers who call a special 800 telephone number for tax information. Suppose that calls to this line occur at a rate of 61 per hour and follow a Poisson distribution. Suppose the IRS workers manning the phone lines can answer an average of 6 calls per hour with the actual service times following an exponential distribution. Assume that 10 IRS workers are available and, when they are all busy, the phone system can keep 5 additional callers on hold. (a) What is the probability that a caller receives a busy signal? (Round your answer to four decimal places.)

During tax season, the IRS hires seasonal workers to help answer the questions of taxpayers who call a special 800 telephone number for tax information. Suppose that calls to this line occur at a rate of 61 per hour and follow a Poisson distribution. Suppose the IRS workers manning the phone lines can answer an average of 6 calls per hour with the actual service times following an exponential distribution. Assume that 10 IRS workers are available and, when they are all busy, the phone system can keep 5 additional callers on hold. (a) What is the probability that a caller receives a busy signal? (Round your answer to four decimal places.)

A First Course in Probability (10th Edition)
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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During tax season, the IRS hires seasonal workers to help answer the questions of taxpayers who call a special 800 telephone. number for tax information. Suppose that calls to this line occur at a rate of 61 per hour and follow a Poisson distribution. Suppose the IRS workers manning the phone lines can answer an average of 6 calls per hour with the actual service times following an exponential distribution. Assume that 10 IRS workers are available and, when they are all busy, the phone system I can keep 5 additional callers on hold. (a) What is the probability that a caller receives a busy signal? (Round your answer to four decimal places.) (b) What is the probability that a caller is put on hold before receiving service? (Round your answer to four decimal places.) (c) On average, how long (in minutes) must a caller wait before speaking with an IRS agent? (Round your answer to two decimal places.) minutes (d) How many additional workers would be required if the IRS wants no more than a 5% chance of a caller receiving a busy signal? At least more workers should be hired.
Transcribed Image Text:During tax season, the IRS hires seasonal workers to help answer the questions of taxpayers who call a special 800 telephone. number for tax information. Suppose that calls to this line occur at a rate of 61 per hour and follow a Poisson distribution. Suppose the IRS workers manning the phone lines can answer an average of 6 calls per hour with the actual service times following an exponential distribution. Assume that 10 IRS workers are available and, when they are all busy, the phone system I can keep 5 additional callers on hold. (a) What is the probability that a caller receives a busy signal? (Round your answer to four decimal places.) (b) What is the probability that a caller is put on hold before receiving service? (Round your answer to four decimal places.) (c) On average, how long (in minutes) must a caller wait before speaking with an IRS agent? (Round your answer to two decimal places.) minutes (d) How many additional workers would be required if the IRS wants no more than a 5% chance of a caller receiving a busy signal? At least more workers should be hired.
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