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 A Level Maths 2.4 Statistical Distributions, covering 2.4.1 Discrete probability distributions, 2.4.2 Binomial distribution as a model, 2.4.3 Calculating binomial probabilities, 2.4.4 Mean and variance of the binomial (A-level only), 2.4.5 Normal distribution as a model (A-level only), 2.4.6 Probabilities using the normal distribution (A-level only), 2.4.7 Links to histograms, mean and standard deviation (A-level only), and 2.4.8 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.