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.
Practise Edexcel A Level Maths The Normal Distribution with exam-style questions for A Level Maths. 100 questions covering The Normal Distribution, Finding Probabilities for Normal Distributions, The Inverse Normal Distribution Function, The Standard Normal Distribution, Finding the mean and standard deviation, Approximating a Binomial Distribution, and Hypothesis Testing with the Normal Distribution, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.