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)
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.