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

$$\begin{array} { l l l l l l l l l } 
5 & 12 & 10 & 8 & 7 & 6 & 9 & 7 & 8
\end{array}$$

(a) Construct a $90 \%$ confidence interval for $\mu$.\\
(b) Comment on the headteacher's claim that the mean time that parents have to wait before seeing a mathematics teacher is 5 minutes.

\hfill \mbox{\textit{AQA S2  Q3}}