The masses of lithium-ion battery packs, B B\,B grams, are distributed such that B∼N(450,152)B \sim \text{N}(450, 15^2)B∼N(450,152).
Five battery packs are selected at random.
Calculate the probability that their total mass exceeds 2280 g.
The masses of industrial sensors, S S\,S grams, are such that S∼N(85,42)S \sim \text{N}(85, 4^2)S∼N(85,42).
Two sensors are selected at random.
Calculate the probability that the magnitude of the difference in their masses is more than 5 g.
The masses of protective housing units, H H\,H grams, are such that H∼N(1200,160)H \sim \text{N}(1200, 160)H∼N(1200,160).
The random variable A A\,A represents the total mass, in g, of a single housing unit packed with 10 sensors, where A A\,A and H H\,H are independent.
Calculate P(A>0.9H+950)P(A > 0.9H + 950)P(A>0.9H+950).
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.