The volumes of chemical reagent in Grade A containers follow a normal distribution with mean 250 ml and standard deviation 4.5 ml. The volumes in Grade B containers follow a normal distribution with mean 242 ml and standard deviation 3.8 ml.
A single container of each grade is selected at random.
Calculate the probability that the Grade A container contains a smaller volume of reagent than the Grade B container.
A laboratory batch is formed by taking 4 Grade A containers and 6 Grade B containers chosen at random.
Determine the probability that the total volume of reagent in the batch is more than 2460 ml.
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.