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.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.