If your cable television goes out, you phone the cable company to get it fixed. Does a real person answer your call? These days, probably not. It is far more likely that you will get an automated response. You will probably be offered several options, such as: to order cable service, press 1; for problems about your bill, press 2; to add new channels, press 3; (and finally) to speak with a customer service agent, press 4. Callers will get frustrated if they have to wait too long before speaking to a live voice. So companies try hard to minimize the time required to connect to a customer service representative.

A large bank decided to study the call response times in its customer service department. The banks goal was to have a representative answer an incoming call within 30 seconds. Here are the results from a random sample of 300 calls to the banks customer service center. Table 10.1 shows the time for the first ring until a customer service agent answers.

Table 10.1 Call center response times (seconds)

59 . 13 . 2 . 24 . 11 . 18 . 38 . 12 . 46 . 17 . 77 . 12 . 46
44 . 4 . 74 . 41 . 22 . 25 . 7 . 10 . 46 . 78 . 14 . 6 . 9
122 . 8 . 16 . 15 . 17 . 17 . 9 . 15 . 24 . 24 . 70 . 9 .9 . 10
32 . 9 . 68 . 8 . 10 . 41 . 13 . 17 . 50 . 12 . 82 . 97 . 33
76 . 56 . 42 . 19 . 14 . 21 . 12 . 44 . 63 . 5 . 21 . 11 . 47
8 . 12 . 4 . 111 . 37 . 12 . 24 . 43 . 37 . 27 . 65 . 32 . 3
9 . 26. 5 . 10 . 30 . 27 . 21 . 14 . 19 . 44 . 49 . 10 . 24
11 . 10 . 22 . 43 . 70 . 27 . 10 . 32 . 96 . 11 . 29 . 7 . 28
22 . 17 . 9 . 24 . 15 . 14 . 34 . 5 . 38 . 29 . 16 . 65 . 6
5 .58 . 17 . 7 . 44 . 14 . 16 . 4 . 46 . 32 . 52 . 75 . 11
11 .17 . 31 . 8 . 36 . 25 . 14 . 85 . 4 . 46 . 23 . 58. 5
54 .28 . 6 . 46 . 4 . 28 . 11 . 111 . 6 . 3 . 83 . 27 . 6
83 . 27 . 2 . 56 . 26 . 21 . 276 . 14 . 30 . 8 . 7 . 12 . 4
29 . 21 . 23 . 4 . 14 . 23 . 22 . 19 . 66 . 51 . 60 . 14 . 111
20 . 7 . 7 . 87 . 22 . 11 . 53 . 20 . 14 . 41 . 30 . 7 . 10
11 . 9 . 9 . 101 . 55 . 18 . 20 . 77 . 14 . 13 . 11 . 22 . 15
2 . 14 . 20 . 83 . 25 . 10 . 34 . 23 . 21 . 5 . 14 . 22 . 10
68 .8 . 70 . 56 . 8 . 26 . 7 . 15 . 7 . 9 . 144 . 11 . 109
20 .4 . 16 . 20 . 124 . 16 . 16 . 47 . 97 . 27 . 61 . 35 . 18
22 .244 . 19 . 10 . 6 . 432 . 20 . 77 . 22 . 7 . 33 . 67 . 20
4 .28 . 5 . 7 . 188 . 18 . 1 . 35 . 78 . 35 . 70 . 85 . 24
333 .50 . 11 . 12 . 11 . 13 . 19 . 16 . 71 . 4 . 63 . 14 . 22
43 .25 . 18 . 55 . 13. 11 . 6 . 13 . 4 . 3 . 17 . 11 . 6 . 17

1. Construct an appropriate graphical display for the call pickup times. Then find out numerical summary statistics. prepare a few sentences describing the distribution of response times.

2. find out and interpret a 95% confidence interval for the mean call pickup time at this bank's customer service department.

3. find out and interpret 95% confidence interval for the proportion of calls coming into this bank's customer service department that were answered within 30 seconds.