4 A wood contains a large number of mature beech trees. The diameters in centimetres of a random sample of 10 of these trees are as follows.
\(\begin{array} { l l l l l l l l l l } 82.6 & 79.2 & 77.8 & 38.4 & 88.1 & 32.2 & 26.5 & 23.4 & 94.3 & 104.2 \end{array}\) A tree surgeon wants to know if the average diameter of mature beech trees in this wood is 50 cm . The tree surgeon produces a Normal probability plot for these data.
\includegraphics[max width=\textwidth, alt={}, center]{4caa7409-cb32-41da-ad64-012a45753296-4_796_1230_589_230}

1. Explain why the tree surgeon should not carry out a test based on the \(t\) distribution.
2. Carry out a suitable test at the \(5 \%\) significance level to investigate whether the average diameter of mature beech trees in this wood is 50 cm .