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 timesfollowing an exponential distribution. Assume that 10 IRS workers are available and, when they are all busy, the phone systemI 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 twodecimal 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 busysignal?At leastmore workers should be hired.

where arrivals follow a Poisson distribution, service times follow an exponential distribution, and…

Answered: During tax season, the IRS hires…

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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Which of the following belongs to lagging indicators A. Manufacturers' new orders B. Stock prices, 500 common stocks C. Average duration of unemployment D. Industrial production
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A burger joint has on average 9 customers arriving per hour. There is only one employee serving customers and she takes about 4 minutes on average to serve a customer. The burger joint is open 10 hours per day and makes a profit of $10 for each burger sold. The staff has a pay rate of $20/hour. Assume a Poisson distribution on the arrival rate of customers and exponential distribution on the service time of the employee. Q. If customers do not want to spend more than 6 minutes in the burger joint (including waiting and service), how much potential profit would the joint lose per day?
(5) A certain educational institute has 15 centers located at different places in a city. There are three telephone operators in each center. The manager wanted to estimate the average number of calls received per telephone per week for this institute. He decided to select four centers and the number of calls received on last week for each operator were recorded. The data collected are given in Table 02. Answer the following questions. Table 02: Number of calls received for each operator 25, 15, 30 18, 12, 10 20, 18, 22 15, 20, 18 Center 1 4 (i) (ii) What is the sampling method used in this study? Justify your answer. Estimate the average number of telephone calls received per telephone operator.
Express House Delivery Service provides high quality service to customers. The company guarantees a refund of all charges if a package it is delivering does not arrive at its destination by the specified time. It is known from past data that despite all efforts, 2% of the packages mailed through this company do not arrive at their destinations within the specified time. Suppose a corporation mails 10 packages through Express House Delivery Service on a certain day.
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Suppose that Mary, Gary, and Larry have been asked to randomly sample 100 patients' visit records from a file of 2000 patient records and record the amount of time the attending physician spent with each patient. Gary suggests the time of year during which the patient was seen may be a confounding variable and strongly advises dividing the year into quarters (Jan - Mar, Apr-Jun, Jul-Sep, Oct- Dec) and randomly selecting 25 patient records from each quarter. Which of the following best describes Gary's sampling plan? (A) A simple random sample (B) A systematic random sample (C) A stratified random sample (D) A cluster sample (E) A convenience sample

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