3 The time, \(T\) minutes, that parents have to wait before seeing a mathematics teacher at a school parents' evening can be modelled by a normal distribution with mean \(\mu\) and standard deviation \(\sigma\).
At a recent parents' evening, a random sample of 9 parents was asked to record the times that they waited before seeing a mathematics teacher.
The times, in minutes, are
$$\begin{array} { l l l l l l l l l }
5 & 12 & 10 & 8 & 7 & 6 & 9 & 7 & 8
\end{array}$$
- Construct a \(90 \%\) confidence interval for \(\mu\).
- Comment on the headteacher's claim that the mean time that parents have to wait before seeing a mathematics teacher is 5 minutes.