A fuel station monitors the amount of petrol dispensed into car tanks. The amount, G G\,G litres, is normally distributed with mean 60 litres. It is known that 10% of cars are dispensed more than 62 litres.
Find the value of k k\,k such that P(k<G<63)=0.40P(k < G < 63) = 0.40P(k<G<63)=0.40.
The pumps are recalibrated so that the standard deviation of the fuel dispensed is 2 litres. After recalibration, the station owner suspects that the mean amount dispensed is less than 60 litres. A random sample of 36 cars is taken, and the mean amount dispensed is found to be 59.4 litres. Test the owner's suspicion at the 5% significance level. State your hypotheses clearly.
351 exam-style questions on AQA A Level Maths 2.4.2 The Normal distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.