A factory produces bags of cement. The weight of a bag of cement is modeled by a normal distribution with mean 50.5 kg50.5\text{ kg}50.5 kg and standard deviation 0.45 kg0.45\text{ kg}0.45 kg.
Find the probability that the weights of two randomly selected bags of cement differ by more than 0.80 kg0.80\text{ kg}0.80 kg.
Bags of cement are randomly selected and loaded onto transport crates. The weight of an empty crate is modeled by a normal distribution with mean 45.0 kg45.0\text{ kg}45.0 kg and standard deviation 1.20 kg1.20\text{ kg}1.20 kg.
Each fully loaded crate contains 20 bags of cement.
Find the probability that the total weight of a randomly selected fully loaded crate is less than 1050 kg1050\text{ kg}1050 kg.
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.