\begin{enumerate}
\item A company that makes ropes for mountaineering wants to assess the breaking strain of its ropes.
- Explain why a sample survey, and not a census, should be used.
- Suggest an appropriate sampling frame.
\item It is thought that a random variable \(X\) has a Poisson distribution whose mean, \(\lambda\), is equal to 8 . Find the critical region to test the hypothesis \(\mathrm { H } _ { 0 } : \lambda = 8\) against the hypothesis \(\mathrm { H } _ { 1 } : \lambda < 8\), working at the \(1 \%\) significance level.
\item A child cuts a 30 cm piece of string into two parts, cutting at a random point.