A company wishes to check on the efficiency of its call centre. It carries out checks on a sample of 200 customer calls by using computer monitoring equipment which measures the length of calls.

1.If the true population mean time per call is 2.3 minutes and the standard deviation 1.28 minutes what is the probability that the mean of this sample will be less than 2.1 minutes?

2.How are we able to answer a. above without knowing whether the population call time distribution is skewed or not?

3.The company has one section which rings people who are not existing customers to advise them of a house-painting service. Call numbers are selected at random from a list of properties in a certain district. From past experience it is known that the chance of a household in this district wanting painting work done is 10%. If a caller rings 12 properties on a particular day what is the chance that exactly two households want painting work done?

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

5.Another part of the call centre deals with queries from existing customers of a photocopier company who mainly ring up requesting service calls to be made. A sample of 56 calls is taken and the average time for them is 5.75 minutes. The population standard deviation is known from past experience to be 1.89 minutes but it is believed that the population mean may have changed from 6 minutes. Use a hypothesis test to test whether the mean call time is still 6 minutes at a 5% level of significance, showing all steps (hypotheses, test statistic, decision rule) and explaining your conclusion in relation to the call centre.