4 Students are each asked to measure the distance between two points to the nearest tenth of a metre.
- Given that the rounding error, \(X\) metres, in these measurements has a rectangular distribution, explain why its probability density function is
$$f ( x ) = \left\{ \begin{array} { c c }
10 & - 0.05 < x \leqslant 0.05
0 & \text { otherwise }
\end{array} \right.$$ - Calculate \(\mathrm { P } ( - 0.01 < X < 0.02 )\).
- Find the mean and the standard deviation of \(X\).