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.
328 exam-style questions on WJEC A Level Maths 4.2 Statistical distributions (A-level only), covering 4.2.1 Statistical distributions (A-level only), 4.2.2 Statistical distributions (A-level only), and 4.2.3 Statistical distributions (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.