In a certain region, 30% of the cars are diesel and 70% are petrol. The mean CO emission of the diesel cars in the region is 0.15 g/km and the mean CO emission of the petrol cars in the region is 0.30 g/km.
Aisha estimates the mean CO emission of the cars in the region by measuring the cars that stop at a motorway service area. Among the cars that stop there, 60% are diesel and 40% are petrol.
Assume that the mean CO emission of the diesel cars stopping at the service area is 0.15 g/km, and that the mean CO emission of the petrol cars stopping there is 0.30 g/km.
Show that the mean CO emission of all the cars in the region is 0.255 g/km.
Find the value that Aisha's method will estimate.
State the size and direction of the resulting error, and explain why measuring far more cars at the service area would not remove it.
28 exam-style questions on AQA A Level Maths 2.1 K: Statistical sampling, covering 2.1.1 Populations, samples and sampling techniques. Each one has a worked solution and a mark scheme showing where the marks go.