2 The times taken for customers' phone complaints to be handled were monitored regularly by a company. During a particular week a researcher checked a random sample of 20 complaints and the times, \(x\) minutes, taken to handle the complaints are summarised by \(\Sigma x = 337.5\). Handling times may be assumed to have a normal distribution with mean \(\mu\) minutes and standard deviation 3.8 minutes.

1. Calculate a \(98 \%\) confidence interval for \(\mu\). During the same week two other researchers each calculated a \(98 \%\) confidence interval for \(\mu\) based on independent samples.
2. Calculate the probability that at least one of the three intervals does not contain \(\mu\).
3. State two ways in which the calculation in part (i) would differ if the standard deviation were unknown.