The volume V V\,V ml of juice in a carton is modelled by V∼N(505,3.782)V\sim N(505,3.78^2)V∼N(505,3.782).
Find the expected number of cartons containing less than 500 ml in a batch of 1000. Give your answer to the nearest whole carton. The population standard deviation will remain 3.78 ml. A regulation requires no more than 1% of cartons to contain less than 500 ml.
Find the minimum population mean that meets the regulation. Give your answer to 3 significant figures. The process mean is set to 509 ml. Later, a random sample of 100 cartons has mean volume 508.37 ml.
Test at the 5% significance level whether there is evidence that the population mean has fallen below 509 ml.
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.