2. The box plot in Figure 1 shows a summary of the weights of the luggage, in kg, for each musician in an orchestra on an overseas tour.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{045e10d2-1766-4399-aa0a-5619dd0cce0f-03_346_1452_324_228}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
The airline's recommended weight limit for each musician's luggage was 45 kg . Given that none of the musicians' luggage weighed exactly 45 kg ,
- state the proportion of the musicians whose luggage was below the recommended weight limit.
A quarter of the musicians had to pay a charge for taking heavy luggage.
- State the smallest weight for which the charge was made.
- Explain what you understand by the + on the box plot in Figure 1, and suggest an instrument that the owner of this luggage might play.
- Describe the skewness of this distribution. Give a reason for your answer.
One musician of the orchestra suggests that the weights of luggage, in kg, can be modelled by a normal distribution with quartiles as given in Figure 1.
- Find the standard deviation of this normal distribution.