A juice company sells two sizes of orange juice cartons. The volume of juice in each carton is normally distributed. A large carton has a mean of 1000 ml and a standard deviation of 12 ml. A small carton has a mean of 240 ml and a standard deviation of 5 ml.
One large carton and 4 small cartons are chosen at random. Find the probability that the volume in the large carton is greater than the total volume in the 4 small cartons.
One large carton and one small carton are chosen at random. Find the probability that the volume in the large carton is less than 4 times the volume in the small carton.
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.