Question

In: Statistics and Probability

During the morning hours at a catalog sales department, telephone calls come in at the rate...

During the morning hours at a catalog sales department, telephone calls come in at the rate (Poisson) of 40 per hour. Calls that cannot be answered immediately are put on hold. The system can handle 8 callers on hold. If additional calls come in, they receive a busy signal. The 3 customer service representatives who answer the calls spend an average of 4 minutes with a customer (Please show how to calculate the trail and error in excel for part a & b).

a. What is the probability that a caller will get a busy signal? (Hint: Solve for log K or ln K using trial and error.)

b. What is the probability that a customer will be put on hold?

Solutions

Expert Solution

orchestra answered 1 year ago
Next > < Previous

Related Solutions

During the early morning hours, customers arrive at a branch post office at an average rate...
During the early morning hours, customers arrive at a branch post office at an average rate of 45 per hour (Poisson), while clerks can handle transactions in an average time (exponential) of 4 minutes each. Fill in the following information: Lq = Avg Number in Line Wq = Avg Time in Line Ws = Avg Time in System For M = 7: Lq = 0.028 Wq = 0.0006 Hours Wq = 0.0373 Minutes Ws = 4.0373 Minutes For M =...
Typical incoming telephone call to your catalog sales force results in a mean order of &28.63...
Typical incoming telephone call to your catalog sales force results in a mean order of &28.63 with a standard deviation of %13.91. You may assume that orders are received independently of one another. 1.An operator is expected to handle 110 incoming calls tomorrow. Find the mean and standard deviation of the resulting total order. 2. Find the approximate probability that the operator in part 1 will generate a total order of more than %3300 tomorrow. 3. Find the approximate probability...
At a call center, calls come in at an average rate of four calls per minute....
At a call center, calls come in at an average rate of four calls per minute. Assume that the time elapsed from one call to the next has the exponential distribution, and that the times between calls are independent. a. Find the average time between two successive calls. b. Find the probability that after a call is received, the next call occurs in less than ten seconds. c. Find the probability that less than five calls occur within a minute....
telephone calls arrive at an exchange have a poisson distribution at an average rate of one...
telephone calls arrive at an exchange have a poisson distribution at an average rate of one every second. Find the probabilities of the following; a. no calls arriving in a given five-second period b. between four and six calls arriving in the five-second period c. there is atleast one call d. there is at most one call
The Ganubrabdrab Company has determined that the number of telephone calls it receives each hour during...
The Ganubrabdrab Company has determined that the number of telephone calls it receives each hour during holidays follows a normal distribution with a mean of 80,000 and a standard deviation of 35,000. Suppose 60 holiday hours are chosen at random. What is the sampling distribution for the 60 hours? What is the probability that for these 60 hours the number of incoming calls will be greater than 91,970? What is the probability that for these 60 hours the number of...
Long-Distance Calls A long-distance provider charges the following rates for telephone calls: Rate Category Daytime (6:00...
Long-Distance Calls A long-distance provider charges the following rates for telephone calls: Rate Category Daytime (6:00 A.M. through 5:59 P.M.) Evening (6:00 P.M. through 11:59 P.M.) Off-Peak (12:00 A.M. through 5:59 A.M.) Rate per Minute $0.07 $0.12 $0.05 Create a C++ program that allows the user to select a rate category and enter the number of minutes of the call, then displays the charges. Use the following test data to determine if the application is calculating properly: Rate Category and...
Assume that the representative will continue to make telephone calls until she makes 2 sales, gets...
Assume that the representative will continue to make telephone calls until she makes 2 sales, gets 5 tentative commitments, or fails to make a sale. Her log for the day consists of a list of calls, with sale, tentative commitment, or no sale noted for each. How many possible logs are there?
Assume that the representative will continue to make telephone calls until she makes 2 sales, gets...
Assume that the representative will continue to make telephone calls until she makes 2 sales, gets 5 tentative commitments, or fails to make a sale. Her log for the day consists of a list of calls, with sale, tentative commitment, or no sale noted for each. How many possible logs are there?
A police department released the numbers of calls for the different days of the week during...
A police department released the numbers of calls for the different days of the week during the month of​October, as shown in the table to the right. Use a 0.01 significance level to test the claim that the different days of the week have the same frequencies of police calls. What is the fundamental error with this​ analysis? Day Sun Mon Tues We Thurs Fri Sat Frequency 155 206 220 244 176 215 240 Calculate the test​ statistic,chi squaredχ2. Calculate...
A police department released the numbers of calls for the different days of the week during...
A police department released the numbers of calls for the different days of the week during the month of​ October, as shown in the table to the right. Use a 0.01 significance level to test the claim that the different days of the week have the same frequencies of police calls. What is the fundamental error with this​ analysis? Day Sun Mon Tues Wed Thurs Fri Sat Frequency 153 210  224 248 174 212 231 Determine the null and alternative hypotheses....
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT