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.
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.