3 During June 2011, the volume, \(X\) litres, of unleaded petrol purchased per visit at a supermarket's filling station by private-car customers could be modelled by a normal distribution with a mean of 32 and a standard deviation of 10 .

1. Determine:
   1. \(\mathrm { P } ( X < 40 )\);
   2. \(\mathrm { P } ( X > 25 )\);
   3. \(\mathrm { P } ( 25 < X < 40 )\).
2. Given that during June 2011 unleaded petrol cost \(\pounds 1.34\) per litre, calculate the probability that the unleaded petrol bill for a visit during June 2011 by a private-car customer exceeded \(\pounds 65\).
3. Give two reasons, in context, why the model \(\mathrm { N } \left( 32,10 ^ { 2 } \right)\) is unlikely to be valid for a visit by any customer purchasing fuel at this filling station during June 2011.
   (2 marks)