A company has three claims representatives who have 8 hour working days, Monday to Friday. Clients come to the offices of the company at a rate of 20 clients per 8 hour day. The time a representative spends to each customer obeys an exponential law with an average service time of 36 minutes. In taking the hour as a unit of time, answer the following questions: (a) How many hours per week is a representative busy on average? (b) What is the average time spent by a customer in the queue before being served by a representative? (c) What is the average number of representatives who are unoccupied? (d) What is the probability that there is a queue?

A company has three claims representatives who have 8 hour working days, Monday to Friday. Clients come to the offices of the company at a rate of 20 clients per 8 hour day. The time a representative spends to each customer obeys an exponential law with an average service time of 36 minutes. In taking the hour as a unit of time, answer the following questions: (a) How many hours per week is a representative busy on average? (b) What is the average time spent by a customer in the queue before being served by a representative? (c) What is the average number of representatives who are unoccupied? (d) What is the probability that there is a queue?

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...

See similar textbooks

Related questions

Q: Median household income sharply increased in 2015 by 5.2% but only grew by 1.8% in 2017 to $61,372.…

A: a) Assume the median income in 2016 is x.

Q: The estimated demand and supply curve for apples is displayed below. If the current price is…

A: Given the current price is $100 / ton . We have to find the demand and supply from the graph and…

Q: A power company charges one household $0.12 per kilowatt-hour (kWh) and $14.89 in monthly taxes.a.…

Q: a. Compute the seasonal index for Spring: b. Compute the seasonal index for Summer: c. Compute the…

A: It is given that M1 = Mean(spring) = 625 M2 = mean(summer) = 475 M3 = mean(fall) = 325 M4 =…

Q: Demand for cars increased by 30% to total of 18% of all cars sold.what is the demand for cars before…

A: It is stated that the demand for cars increased to 18%. The increase in the demand (in percentage)…

Q: for january 1, 2001 to january 1, 2008, the population of florida grew from 17 million to 19.3…

Q: Suppose the population of a town is 8,600 and is growing 3% each year. Predict the population after…

A: Population in 1 year = 8600 + 8600*3/100 =8858 Population…

Q: Let T be the number of years since 1988. What does t = 12 mean in this situation?

A: It is given that T is the number of years since 1988.

Q: The monthly usage for a component supplied to a medical equipment manufacturing plant is 4718 parts.…

Q: Calculate the months supply of warehouse speace in a market that absorbed 45000 square feet last…

A: Total supply in the last year = 145,000 vacant square feet =10,000 Out of that are ; in monthly…

Q: If 5.2% of the 200 million adult Americans are unemployed, how many adult Americans are unemployed?…

Q: Why is there a need to convert the hours into minutes?

A: The explanation is as follows:

Q: Suppose you are a pharmacist and a customer asks you thefollowing question. His child is to receive…

A: Given: Total nausea medicine received by child=13.5 mlTotal time period=54 hours To Find: The amount…

Q: If 150 mL is removed from a bag which contains 500 mL of glucose 5% and replaced with 150 mL of…

A: Step 1: Calculate the amount of glucose in the initial solution.The initial solution has a volume of…

Q: A Computer on the 4 Mbps network is regulated by a token bucket. The bucker is filled at a rate of…

A: Let T be the time taken by computer to transmit full 6Mbps Let c = initial capacity =8Mb r =filling…

Q: the length of time taken to run 100m a continous data?

A: Variables is of two types: qualitative data and quantitative data. Qualitative data represents…

Q: Use the following information to answer the exercise: In a survey of 100 stocks on NASDAQ, the…

A: Question:

Q: Estimate the population based on T Total Tagged = 60 t tagged recaught number 15 P total recaught…

A: Given T total tagged = 60 t tagged recaught number =15 p total recaught=250 Estimated population =…

Q: At inventory time, 435 pounds of magnet wire for winding motors is available. In ten successive…

Q: . At the Franklin Post Office, patrons wait in a singleline for the first open window. On average,…

A: Given: The average rate of the customers entering the system=100/ hr The service rate=45/hr…

Q: There are approximately 3,000 bass in a lake. The population grows at a rate of 2% per year. Round…

A: The average rate of change is defined as a measure of how much a function change per unit on an…

Q: 1. Use the change of base formula to compute b. log; 5 a. logs 6 Ad. log 7 c. log3 7

Q: A research assistant has been tasked to update 12000 records in a database. She aims to do the task…

A: Data is the data and the base is where it is stored or how it is stored. A Database is a systematic…

Q: An automotive technician spent 1/3 changing spark plugs 1/4 changing an air filter and 1/4 changing…

Question

(a)

How many hours per week is a representative busy on average?

(b)

What is the average time spent by a customer in the queue before being served by a representative?

(c)

What is the average number of representatives who are unoccupied?

(d)

What is the probability that there is a queue?

Video Video

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1: Calculate Average time a representative is busy per week

VIEW

Step 2: Calculate Average Waiting Time

VIEW

Step 3: Calculate average number of representatives

VIEW

Step 4: Calculate probability that there is a queue

VIEW

Solution

VIEW

Step by step

Solved in 5 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

During a typical year at a certain state fair, milk sales total 70,000 gallons. (a) If the fair runs for 10 days, determine the average number of gallons sold each day. (b) How many 8-ounce cups per day would this be? (c) If 1 cup of milk costs $1.25, how much money (in dollars) per day is made in milk sales?
An office allots 85,000 a month for operational expenses such that 3/5 is allotted to the basic salaries 3/16 is allotted to the technical aspect, and 1/16 is allotted to supplies. How much is allotted to each of the expenses?
How many times more intense is an earthquake of magnitude 8.2 than an earthquake of magnitude 7.5?
There are initially 340 cells present in a colony of bacteria. This strain of bacteria grows by 22% every 3.5 hours. Assuming that this growth continues in this man- ner, determine the following. How many bacteria cells will be present in the colony after 24 hours? How long will it take for the colony to reach 5000 bacteria cells? Round each response to the nearest whole number. bacteria cells hours.
(1) The rate of data transfer from an internet provider is 2300bytes per second. How long will it take to transfer a 387000 bytes document. (2) a long distance phone company charged 6.8 cents per minute, how many minutes did he spend if the total bill is $ 23.80
Samsan Tech, had been mailing out coupons for sale of shares at a constant rate for 4 days, when they counted the coupons, they still had mail out and discover they had 120,000 left. After 7 total days of work they had 75,000 left. At what rate are they mailing coupons out? a. 17,000 coupons per day b. 15,000 coupons per day c. 11,000 coupons per day d. 13,000 coupons per day
Assume you have a pasture with a carrying capacity of 96 AUMS, and average annual production of 180 tons of forage. How many sheep can graze this pasture for six months?
The US Census Bureau determined that from 1910 to 2010 the US population increased by approximately 1.5% each year. The 13th US Census (conducted in 1910) determined that the US population was 92.228 million people. What is the 6-year growth factor? What was the population of the United States in 1916 ? The population in 1966 is how many times as large as the population in 1960 ? Determine in what year the population of the United States was 141.04 million people.
If tacomas population in 2000 is 200,000 and it grows by 8% a year, what is the population in 2012?
Which values should you plot to show a linear relationship? Month Population Log(population) 1 1400 3.146 2600 3.415 4700 3.672 4 9000 3.954 17000 4.230 6. 32000 4.505 2. 3. 寸 5.
Answer the following: (Note: only use 1 decimal place for the answer) In a community with a population of 1M people where 65% are female, 100,000 babies were born during the year 2010. Out of the number of mothers who gave birth, 769 mothers died during childbirth. a total of 90 babies died during labor. Calculate the maternal mortality rate per 100,000 population