a. After a change in the process for managing customer enquiries posted to their website, a company is concerned that it is taking too long to respond. It collects data on the time taken to respond for a sample of 400 customer enquiries. If the true population mean response time is 27.6 minutes with the standard deviation being 16 minutes, what is the probability that the mean of this sample will be less than 25.6 minutes? b. How are we able to answer a. above without knowing whether the population call time distribution is skewed or not? c. The company randomly selects a number of registered customers. It calls these customers asking them to complete a customer satisfaction survey by phone. From previous surveys, the company knows that the chance of a selected customer agreeing to complete the survey is 20%. If in one day it calls 14 selected customers, what is the chance that exactly 4 customers complete the survey?

d. What assumptions did you need to make to answer c.? Answer in relation to this particular situation.

e. The company has a complaints telephone line. The company is concerned that because of changes to their website, more lengthy complaints calls are being received. A sample of 100 calls is taken. Their average is 7.25 minutes. The population mean is known to have been 7 minutes with a standard deviation of 2.1 minutes. Use a hypothesis test to test if the mean call time has changed from 7 minutes at the 1% level of significance. Show all steps (hypotheses, test statistic, decision rule) and explain your conclusion.