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.
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.