3 A fair cubical die with faces numbered \(1,1,1,2,3,4\) is thrown and the score noted. The area \(A\) of a square of side equal to the score is calculated, so, for example, when the score on the die is 3 , the value of \(A\) is 9 .

1. Draw up a table to show the probability distribution of \(A\).
2. Find \(\mathrm { E } ( A )\) and \(\operatorname { Var } ( A )\).
3. In a spot check of the speeds \(x \mathrm {~km} \mathrm {~h} ^ { - 1 }\) of 30 cars on a motorway, the data were summarised by \(\Sigma ( x - 110 ) = - 47.2\) and \(\Sigma ( x - 110 ) ^ { 2 } = 5460\). Calculate the mean and standard deviation of these speeds.
4. On another day the mean speed of cars on the motorway was found to be \(107.6 \mathrm {~km} \mathrm {~h} ^ { - 1 }\) and the standard deviation was \(13.8 \mathrm {~km} \mathrm {~h} ^ { - 1 }\). Assuming these speeds follow a normal distribution and that the speed limit is \(110 \mathrm {~km} \mathrm {~h} ^ { - 1 }\), find what proportion of cars exceed the speed limit.