Easy -1.8 This is a straightforward systematic sampling question requiring only basic arithmetic (720รท40=18) and understanding of the definition. Parts (a)-(c) are direct recall/calculation with no problem-solving, and part (d) is standard bookwork about sampling methods. Significantly easier than average A-level questions.
The names of the 720 members of a swimming club are listed alphabetically in the club's membership book. The chairman of the swimming club wishes to select a systematic sample of 40 names. The names are numbered from 001 to 720 and a number between 001 and \(w\) is selected at random. The corresponding name and every \(x\) th name thereafter are included in the sample.
Find the value of \(w\).
Find the value of \(x\).
Write down the probability that the sample includes both the first name and the second name in the club's membership book.
State one advantage and one disadvantage of systematic sampling in this case.
\begin{enumerate}
\item The names of the 720 members of a swimming club are listed alphabetically in the club's membership book. The chairman of the swimming club wishes to select a systematic sample of 40 names. The names are numbered from 001 to 720 and a number between 001 and $w$ is selected at random. The corresponding name and every $x$ th name thereafter are included in the sample.\\
(a) Find the value of $w$.\\
(b) Find the value of $x$.\\
(c) Write down the probability that the sample includes both the first name and the second name in the club's membership book.\\
(d) State one advantage and one disadvantage of systematic sampling in this case.\\
\end{enumerate}
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\hfill \mbox{\textit{Edexcel S3 2018 Q1 [5]}}