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 A Level Maths 2.4 Statistical Distributions, covering 2.4.1 Discrete probability distributions, 2.4.2 Binomial distribution as a model, 2.4.3 Calculating binomial probabilities, 2.4.4 Mean and variance of the binomial (A-level only), 2.4.5 Normal distribution as a model (A-level only), 2.4.6 Probabilities using the normal distribution (A-level only), 2.4.7 Links to histograms, mean and standard deviation (A-level only), and 2.4.8 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.