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 questions about your bill, press 2; to add new channels, press 3; (and finally) to speak with a customer service agent, press 4. Customers will get frustrated if they have to wait too long before speaking to a live person. 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 bank's goal was to have a representative answer an incoming call in less than 30 seconds. The figure below is a histogram of the response times in a random sample of 241 calls to the bank's customer service center in a given month.

Describe the distribution (shape, center, and spread) of call response times for the random samples of 241 calls. 

1. 1. About what proportion of the call response times in the sample were less than 30 seconds? Explain.
   2. The bank's manager would like to estimate the true proportion p of calls to the bank's customer service center that are answered in less than 30 seconds.
      
      • (a) What conditions must be met to calculate a 95% confidence interval for p? show that the conditions are met in this case.
      • (b) Explain the meaning of 95% in this setting. 
      • (c) A 95% confidence interval for p is (0.783, 0.877). Give the margin of error and show how it was calculated. 
      • (d) Interpret the interval from part (c) in context. 
   3. Construct and interpret a 95% confidence interval for the true mean response time of calls to the bank's customer service center.
   4. Is the customer service center meeting its goal of answering calls in less than 30 seconds? Give appropriate evidence to support your answer. 
   5. If the service center is meeting its goals, what do you think is being done to ensure this happens? If the service center is not meeting its goals, what can be changed or implemented to make sure they do?

 

35 30 25 10 0.0 7.5 15.0 22.5 30.0 37.5 45.0 10 20 30 40 Call response time (seconds) Call response time (seconds)