A drone delivery company, AirLift, categorizes items into two types: Priority (PPP) and Standard (SSS). The masses, in grams, of Priority packages are distributed as P∼N(820,202)P \sim \text{N}(820, 20^2)P∼N(820,202) and the masses of Standard packages are distributed as S∼N(610,122)S \sim \text{N}(610, 12^2)S∼N(610,122).
A Priority package and a Standard package are selected at random. Determine the probability that the mass of the Priority package is less than 135%135\%135% of the mass of the Standard package.
Two Standard packages are chosen at random. Find the probability that the absolute difference between their masses is more than 181818 g.
AirLift uses protective shipping crates to transport goods. Each crate contains either 666 Priority packages or 888 Standard packages. The mass of an empty shipping crate, MMM, is distributed as M∼N(150,102)M \sim \text{N}(150, 10^2)M∼N(150,102). Determine the probability that a crate of 888 Standard packages has a greater total mass than a crate of 666 Priority packages.
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.