\begin{question}
The following figure shows a scatterplot. Which of the
following statements are correct?
\setkeys{Gin}{width=0.7\textwidth}
\includegraphics{scatterplot-002}
\begin{answerlist}
\item The absolute value of the correlation coefficient is at most $0.8$.
\item The standard deviation of $X$ is at least $6$.
\item For $X = 17.1 $, $Y$ can be expected to be about 19.9 .
\item The scatterplot is standardized.
\item The mean of $Y$ is at least $30$.
\end{answerlist}
\end{question}
\begin{solution}
\begin{answerlist}
\item False. A strong association between the variables is given in the scatterplot. Hence the absolute value of the correlation coefficient is close to $1$ and therefore larger than $0.8$.
\item True. The standard deviation of $X$ is about equal to $ 20 $ and is therefore larger than $6$.
\item True. The regression line at $X=17.1$ implies a value of about $Y = 19.9$.
\item False. The scatterplot is not standardized, because $X$ and $Y$ do not both have mean $0$ and variance $1$.
\item False. The mean of $Y$ is about equal to $ 20 $ and hence is smaller than $30$.
\end{answerlist}
\end{solution}
%% META-INFORMATION
%% \extype{mchoice}
%% \exsolution{01100}
%% \exname{Scatterplot}