4 A digital thermometer measures temperatures in degrees Celsius. The thermometer rounds down the actual temperature to one decimal place, so that, for example, 36.23 and 36.28 are both shown as 36.2 . The error, \(X ^ { \circ } \mathrm { C }\), resulting from this rounding down can be modelled by a rectangular distribution with the following probability density function. $$f ( x ) = \left\{ \begin{array} { l c } k & 0 \leqslant x \leqslant 0.1
0 & \text { otherwise } \end{array} \right.$$

1. State the value of \(k\).
2. Find the probability that the error resulting from this rounding down is greater than \(0.03 ^ { \circ } \mathrm { C }\).
3. 1. State the value for \(\mathrm { E } ( X )\).
   2. Use integration to find the value for \(\mathrm { E } \left( X ^ { 2 } \right)\).
   3. Hence find the value for the standard deviation of \(X\).
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