## The Environment Protection Agency has developed a testing programme to monitor petrol vehicle emission: foundation maths Course Work, UO, UK

Question 3 [5 marks]
The Environment Protection Agency has developed a testing programme to monitor petrol vehicle emission levels of several pollutants. Data collected under a variety of conditions suggests that the Normal curve provides an adequate approximation for the distribution of the key variable of interest, the amount of oxides of nitrogen (g/mile) emitted by a vehicle. The mean emission is 1.7 g/mile, with a standard deviation of 0.48 g/mile.

a) Calculate the probability that a randomly selected petrol vehicle emits more than 0.88 g/mile.

b) Calculate the proportion of petrol vehicles that are expected to emit between 1.0 and 2.0 g/mile.

c) Calculate the upper permissible limit on vehicle pollution, defined by the agency to be the amount that only 1% of petrol vehicles exceed.

d) An ecological monitoring group proposes that a progressive pollution tax is introduced as follows. For each vehicle, the pollution level should be measured and the appropriate taxes would be payable:
below                                                        1.0 g/mile                                   no tax
between                                                  1.0 and 1.6 g/mile                   £50
between                                                  1.6 and 2.2 g/mile                   £100
between                                                 2.2 and 2.8 g/mile                   £250
above                                                      2.8 g/mile                                     £2000
Assuming there are 15 million petrol vehicles in the UK, and their emissions follow the above model, how much tax would be raised in total if this proposal was implemented?