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.

i) true population mean time per call = 2.3 minutes, standard deviation = 1.28 minutes.

what is the probability that the mean of this sample will be less than 2.1 minutes?

ii) how do we answer i) without knowing if the population call time distribution is skewed or not?

iii) company has a section that rings people who are not existing customers and tells them about a house painting service. phone numbers are randomly selected from lists of houses in particular districts. from previous experience we know that the chance of a household in the area wanting painting done is 10%. So if the caller calls 12 properties on a certain day then what is the chance that exactly 2 houses want the painting work done?

iv) what assumptions did we need to make to answer above iii)? give the answer in relation to the specific situation.

v) another area of the centre looks after queries from current customers of a photocopier company, who usually ring up requesting service calls to be made. A sample of 56 calls is taken.

Average call time = 5.75mins

population standard deviation = 1.89 mins

note that the population mean may have changed from 6 mins as per past experience.

Using a hypothesis test, test if the mean call time is still 6 mins with a 5% level of significance.

show ALL steps - hypotheses, test statistic, decision rule

explain your conclusion in direct relation to this call centre situation.