![Problem 6: 10 points John is a customer service representative who responds to the calls. The number of calls during one shift is (N + 1), where is Poisson distributed with the expected value-λ = 24, the duration, U, of a single call (in minutes) is uniformly distributed over the interval (2,8) N+1 Suppose that T- X, represents the actual time spent by John with customers on the phone. 1. Evaluate the average busy time, E T], for John 2. Determine the variance, Var [T], of this busy time.](http://img.homeworklib.com/questions/81f9f560-785c-11ea-a968-5f914baacdf0.png?x-oss-process=image/resize,w_560)
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Problem 6: 10 points John is a customer service representative who responds to the calls. The...
Problem 5: 10 points Assume that a mumber N of phone calls handled by a customer...
Problem 5: 10 points Assume that a mumber N of phone calls handled by a customer service representative during one 8-hour shift is Poisson distributed with rate = A = 5 calls per shift. Duration T ofa randomly selected call in minutes is uniformly distributed over the interval (4, 10). Duration values (Th : k = 1,2,.,} do not depend on N. Consider the total time spent on conversations with customers, s-ΣΤ 1. Evaluate expected value of S 2. Determine...
Let T denote the time in minutes for a customer service representative to respond to 10...
Let T denote the time in minutes for a customer service representative to respond to 10 telephone inquiries. T is uniformly distributed on the interval with endpoints 8 minutes and 12 minutes. Let R denote the average rate, in customers per minute, at which the representative responds to inquiries. 4. Which of the following is the density function of the random variable R on the interval 10 10 12 (B) 3-5 (c) 3r SIn(r) D)7 CE) 2r 10
Phone calls that come to the customer service number are independent. Average waiting time until the...
Phone calls that come to the customer service number are independent. Average waiting time until the fifth phone call is 10 minutes. a.Find the average waiting time between any two consecutive phone calls. b. Find the variance of the waiting time until the fifth phone call to customer service .c. Find the variance of the waiting time until the first phone call to customer service. d. Find the 80th percentile of the waiting time until the first phone call.
Phone calls that come to the customer service number are independent. Average waiting time until the...
Phone calls that come to the customer service number are independent. Average waiting time until the fifth phone call is 10 minutes. a.Find the average waiting time between any two consecutive phone calls. b. Find the variance of the waiting time until the fifth phone call to customer service .c. Find the variance of the waiting time until the first phone call to customer service. d. Find the 80th percentile of the waiting time until the first phone call.
A call center is concerned that call durations for a customer service representative are too erratic:...
A call center is concerned that call durations for a customer
service representative are too erratic: high variations is call
durations can lead to customer dissatisfaction who have to wait
longer for a resolution. The company has collected data from 24
randomly selected phone calls from that specific customer
representative and found that s = 4.15 minutes. Answer the
following questions.
(a) Is there enough evidence to suggest that σ = 4 minutes? Use
α = 0.05.
(b) Assume that...
1. A customer service representative must spend different amounts of time with each customer to resolve...
1. A customer service representative must spend different amounts of time with each customer to resolve various concerns. The amount of time spent with each customer can be modeled by the following distribution: X ~ Exp(0.2) Find P(x > 4) a. 0.225 b. 0.449 c. 0.551 d. 0.635 2. At an urgent care facility, patients arrive at an average rate of one patient every seven minutes. Assume that the duration between arrivals is exponentially distributed. Find the probability that the...
1. A customer service representative must spend different amounts of time with each customer to resolve...
1. A customer service representative must spend different amounts of time with each customer to resolve various concerns. The amount of time spent with each customer can be modeled by the following distribution: X ~ Exp(0.2) Find median. Round to the nearest a. 3.5 b. 7 c. 5 d. 2.5 2. Suppose you arrive into a building and are about to take an elevator to the your floor. Once you call the elevator, it will take between 2 and 40...
HELP 19. (10 points) Barrington do not want to house customer service ce echnology Group handles customer service calls for companies who nters in-house. Barrington has five call handlers and per...
HELP
19. (10 points) Barrington do not want to house customer service ce echnology Group handles customer service calls for companies who nters in-house. Barrington has five call handlers and per year. Each call handler can process 10,000 calls per year. Barringion 000. Variable cost per call taken is has developed a software that allows customers s get answers to their questions and complaints online, reducing the number of calls processed per year to 45 $1.50 a) What is Barrington's...
Problem 5: 10 points Consider a service station with N- 8 servers. Customer arrivals form a...
Problem 5: 10 points Consider a service station with N- 8 servers. Customer arrivals form a Poisson process with the rate ? = 7 per hour. However, if there is a vacant seat (that is if the number of customers ongoing their services is n S 7, then the new customer begins the service. However, if n 8, the new customer leaves the system Individual service times are independent exponentially distributed with the mean t o20 minutes. 1. Describe the...
The duration t (in minutes) of customer service calls received by a certain company is given...
The duration t (in minutes) of customer service calls received by a certain company is given by the following probability density function (Round your answers to four decimal places.) f(t) - 0.5e-0.st, 20 (a) Find the probability that a call selected at random lasts 2 minutes or less, (b) Find the probability that a call selected at random lasts between 7 and 12 minutes. (c) Find the probability that a call selected at random lasts 2 minutes or less given...
Problem 5: 10 points Assume that a mumber N of phone calls handled by a customer service representative during one 8-hour shift is Poisson distributed with rate = A = 5 calls per shift. Duration T ofa randomly selected call in minutes is uniformly distributed over the interval (4, 10). Duration values (Th : k = 1,2,.,} do not depend on N. Consider the total time spent on conversations with customers, s-ΣΤ 1. Evaluate expected value of S 2. Determine...
Let T denote the time in minutes for a customer service representative to respond to 10 telephone inquiries. T is uniformly distributed on the interval with endpoints 8 minutes and 12 minutes. Let R denote the average rate, in customers per minute, at which the representative responds to inquiries. 4. Which of the following is the density function of the random variable R on the interval 10 10 12 (B) 3-5 (c) 3r SIn(r) D)7 CE) 2r 10
A call center is concerned that call durations for a customer
service representative are too erratic: high variations is call
durations can lead to customer dissatisfaction who have to wait
longer for a resolution. The company has collected data from 24
randomly selected phone calls from that specific customer
representative and found that s = 4.15 minutes. Answer the
following questions.
(a) Is there enough evidence to suggest that σ = 4 minutes? Use
α = 0.05.
(b) Assume that...
HELP
19. (10 points) Barrington do not want to house customer service ce echnology Group handles customer service calls for companies who nters in-house. Barrington has five call handlers and per year. Each call handler can process 10,000 calls per year. Barringion 000. Variable cost per call taken is has developed a software that allows customers s get answers to their questions and complaints online, reducing the number of calls processed per year to 45 $1.50 a) What is Barrington's...
Problem 5: 10 points Consider a service station with N- 8 servers. Customer arrivals form a Poisson process with the rate ? = 7 per hour. However, if there is a vacant seat (that is if the number of customers ongoing their services is n S 7, then the new customer begins the service. However, if n 8, the new customer leaves the system Individual service times are independent exponentially distributed with the mean t o20 minutes. 1. Describe the...
The duration t (in minutes) of customer service calls received by a certain company is given by the following probability density function (Round your answers to four decimal places.) f(t) - 0.5e-0.st, 20 (a) Find the probability that a call selected at random lasts 2 minutes or less, (b) Find the probability that a call selected at random lasts between 7 and 12 minutes. (c) Find the probability that a call selected at random lasts 2 minutes or less given...
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