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Let T denote the time in minutes for a customer service representative to respond to 10...
Problem 6: 10 points John is a customer service representative who responds to the calls. The...
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....
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...
Suppose that the average waiting time at a banking service is 10 minutes. A customer waited...
Suppose that the average waiting time at a banking service is 10 minutes. A customer waited for 10 minutes, find the probability that he will be still waiting after 30 minutes. What is the approximate probability that the average waiting time of the next 25 customers is at most 12 minutes?
11 a) Find the conditional density of T; given that there are 10 arrivals in the...
11
a) Find the conditional density of T; given that there are 10 arrivals in the time interval (0,1). b) Find the conditional density of Ts given that there are 10 arrivals in the time interval (0,1). c) Recognize the answers to a) and b) as named densities, and find the parameters. 11. Suppose X has uniform distribution on (-1,1) and, given X = 1, Y is uniformly distributed on (-V1-22. - 7?). Is (X,Y) then uniformly distributed over the...
The arrival time t(in minutes) of a bus at a bus stop is uniformly distributed between 10:00 A.M. and 10:03 A.M.
The arrival time t(in minutes) of a bus at a bus stop is uniformly distributed between 10:00 A.M. and 10:03 A.M. (a) Find the probability density function for the random variable t. (Let t-0 represent 10:00 A.M.) (b) Find the mean and standard deviation of the the arrival times. (Round your standard deviation to three decimal places.) (с) what is the probability that you will miss the bus if you amve at the bus stop at 10:02 A M ? Round your answer...
3.48. At Samantha's Super Store, the customer service area processes customer returns, answers customer questions a...
3.48. At Samantha's Super Store, the customer service area processes customer returns, answers customer questions and provides inform- ation, addresses customer complaints, and sells gift certificates. The manager believes that if customers must wait longer than 8 minutes to see a customer service representative they get very irritated. The cus- tomer service process has been designed to achieve a customer wait time of between 6 and 12 minutes. The store manager has conducted 10 samples of five observations each of...
3. Construc t a stem-and-leaf display for the following data, which give the times (in minutes)...
3. Construc t a stem-and-leaf display for the following data, which give the times (in minutes) of 24 customers spent waiting to speak to a customer service representative when they called about problems with their internet service provider. (8 points) 12 15 7 29 32 16 10 14 17 8 19 2 4 14 22 25 18 6 22 16 13 16 12 20 2
HW16 Saved Help Save & Exit Sub Check my work Exercise 9.8 (Algo) THE BANK CUSTOMER...
HW16 Saved Help Save & Exit Sub Check my work Exercise 9.8 (Algo) THE BANK CUSTOMER WAITING TIME CASE points Recall that a bank manager has developed a new system to reduce the time customers spend waiting to be served by tellers during peak business hours. The mean waiting time during peak business hours under the current system is roughly 9 to 10 minutes. The bank manager hopes that the new system will have a mean waiting time that is...
A critically important aspect of customer service in a supermarket is the waiting time at the...
A critically important aspect of customer service in a supermarket is the waiting time at the checkout (defined as the time the customer enters the line until he or she is served). Data were collected during time periods in which a constant number of checkout counters were open. The total number of customers in the store and the waiting time (in minutes) were recorded. . Determine the coefficient of determination, r 2 , and interpret its meaning. 6. How useful...
10. Prove the following theorem Theorem 1 Let H and H denote the input-output transfer functions for the continuous tim...
10. Prove the following theorem Theorem 1 Let H and H denote the input-output transfer functions for the continuous time systems associated with state matrices (A, B, C) and (A, B,C), respectively. Thus the systems have state representations (t) = Ar(t)+Bu(t) t)C(t) 1(t y(t) and Ci(t) = Assume system (A B. C) and (A. B,C) are equivalent representations, and hence there erists an invertible matriz P such that i(t) = Pa (t) defines a coordinate transformation between the two systems...
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....
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...
11
a) Find the conditional density of T; given that there are 10 arrivals in the time interval (0,1). b) Find the conditional density of Ts given that there are 10 arrivals in the time interval (0,1). c) Recognize the answers to a) and b) as named densities, and find the parameters. 11. Suppose X has uniform distribution on (-1,1) and, given X = 1, Y is uniformly distributed on (-V1-22. - 7?). Is (X,Y) then uniformly distributed over the...
3.48. At Samantha's Super Store, the customer service area processes customer returns, answers customer questions and provides inform- ation, addresses customer complaints, and sells gift certificates. The manager believes that if customers must wait longer than 8 minutes to see a customer service representative they get very irritated. The cus- tomer service process has been designed to achieve a customer wait time of between 6 and 12 minutes. The store manager has conducted 10 samples of five observations each of...
3. Construc t a stem-and-leaf display for the following data, which give the times (in minutes) of 24 customers spent waiting to speak to a customer service representative when they called about problems with their internet service provider. (8 points) 12 15 7 29 32 16 10 14 17 8 19 2 4 14 22 25 18 6 22 16 13 16 12 20 2
HW16 Saved Help Save & Exit Sub Check my work Exercise 9.8 (Algo) THE BANK CUSTOMER WAITING TIME CASE points Recall that a bank manager has developed a new system to reduce the time customers spend waiting to be served by tellers during peak business hours. The mean waiting time during peak business hours under the current system is roughly 9 to 10 minutes. The bank manager hopes that the new system will have a mean waiting time that is...
10. Prove the following theorem Theorem 1 Let H and H denote the input-output transfer functions for the continuous time systems associated with state matrices (A, B, C) and (A, B,C), respectively. Thus the systems have state representations (t) = Ar(t)+Bu(t) t)C(t) 1(t y(t) and Ci(t) = Assume system (A B. C) and (A. B,C) are equivalent representations, and hence there erists an invertible matriz P such that i(t) = Pa (t) defines a coordinate transformation between the two systems...
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