1 Josephine accurately measures the widths of A4 sheets of paper and then rounds the widths to the nearest 0.1 cm . The rounding error, \(X\) centimetres, follows a rectangular distribution. A randomly selected A4 sheet of paper is measured to be 21.1 cm in width.

1. Write down the limits between which the true width of this A4 sheet of paper lies.
   (1 mark)
2. Write down the value of \(\mathrm { E } ( X )\) and determine the exact value of the standard deviation of \(X\).
3. Calculate \(\mathrm { P } ( - 0.01 \leqslant X \leqslant 0.03 )\).