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.
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.