A commercial bakery produces two types of loaves: Sourdough and Rye. The weights of Sourdough loaves, SSS grams, and Rye loaves, RRR grams, are independently normally distributed such that
S∼N(820,152)andR∼N(780,122) S \sim \text{N}(820, 15^2) \quad \text{and} \quad R \sim \text{N}(780, 12^2) S∼N(820,152)andR∼N(780,122)Find the probability that the weights of 2 randomly selected Sourdough loaves will differ by more than 20 g.
Find the probability that the weight of a randomly selected Rye loaf is less than 0.95 of the weight of a randomly selected Sourdough loaf.
Loaves are packed into crates. Each crate contains either 10 randomly selected Sourdough loaves or 10 randomly selected Rye loaves. The weight of an empty crate has distribution N(1500,302)\text{N}(1500, 30^2)N(1500,302).
Find the probability that a full crate of Sourdough loaves weighs at least 450 g more than a full crate of Rye loaves.
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.