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.
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.