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.
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.