A call center is open from 8am in the morning until 5pm in the afternoon Monday to Friday. It is a small center with only one person answering phone calls. If a person is calling while the operator is busy they are put on hold. The call center decides to give a new caller some information on the expected waiting time. The information provided should be a message like this:
“Your call is very important to us. Our representative is currently busy with another customer. You are the next person in line, and your expected wait time is between 1 and 5 minutes”
or maybe
“Your call is very important to us. Our representative is currently busy with other customers. You are caller number 3 in line, and your expected wait time is between 15 and 27 minutes”
In order to figure out the wait times they keep track of all calls and waiting times for one month (24 working days).
You can get the data with
source("http://academic.uprm.edu/wrolke/esma5015/queuedata.txt")Here it what the start looks like:
kable.nice(head(Days[[1]]))| Times | Events |
|---|---|
| 8:21AM | C |
| 8:27AM | C |
| 8:31AM | F |
| 8:36AM | F |
| 8:38AM | C |
| 8:44AM | F |
this tells us that on day 1 the first call came in at 8:21 AM. It lasted until 8:31 AM. There was also a call coming in at 8:27 AM, so by the time the first call was finished there was 1 customer waiting in line.
At the end of day 1 we find
kable.nice(tail(Days[[1]]))| Times | Events | |
|---|---|---|
| 95 | 4:16PM | F |
| 96 | 4:22PM | F |
| 97 | 4:36PM | C |
| 98 | 4:44PM | C |
| 99 | 5:01PM | F |
| 100 | 5:14PM | F |
As we can see, the last call was accepted just before 5 pm but those already on line were still getting taken care off (nice!)
Use the data provided and write a computer program that finds a 95% confidence interval for a person who is \(n^{th}\) in line and who calls in when the customer rep has already talked \(k\) minutes with the current customer.