The volume of liquid delivered by a high-precision agricultural drone, V V\,V litres, is normally distributed such that V∼N(12.5,0.62)V \sim \text{N}(12.5, 0.6^2)V∼N(12.5,0.62).
Five drones are selected at random to spray a field.
Calculate the probability that their combined volume is greater than 64.0 litres.
The concentration of a specific reagent in pharmaceutical vials, C C\,C mg/L, is distributed such that C∼N(45.0,1.22)C \sim \text{N}(45.0, 1.2^2)C∼N(45.0,1.22).
Two vials are selected at random from the production line.
Calculate the probability that the magnitude of the difference in their reagent concentrations exceeds 1.5 mg/L.
The mass of a specialized shipping frame, H H\,H kg, follows the distribution H∼N(20.0,0.5)H \sim \text{N}(20.0, 0.5)H∼N(20.0,0.5).
The random variable T T\,T represents the total weight of a fully assembled unit comprising one frame, whose mass is independent of HHH, packed with 12 electronic components, where each component has a mass K∼N(5.2,0.152)K \sim \text{N}(5.2, 0.15^2)K∼N(5.2,0.152) kg.
Given that T T\,T and H H\,H are independent,
Calculate P(T<0.8H+68.0)P(T < 0.8H + 68.0)P(T<0.8H+68.0)
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.