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).
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.