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.
390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.