The masses of boxes of apples, A A\,A kg, are distributed such that A∼N(1.5,0.042)A \sim \text{N}(1.5, 0.04^2)A∼N(1.5,0.042).
Four boxes of apples are selected at random.
Calculate the probability that their total mass is less than 5.9 kg.
The masses of bags of pears, P P\,P kg, are such that P∼N(0.8,0.052)P \sim \text{N}(0.8, 0.05^2)P∼N(0.8,0.052).
Two bags of pears are selected at random.
Calculate the probability that the magnitude of the difference in their masses is more than 0.06 kg.
The masses of shipping crates, C C\,C kg, are such that C∼N(4.0,0.08)C \sim \text{N}(4.0, 0.08)C∼N(4.0,0.08).
The random variable G G\,G represents the total mass, in kg, of a single crate packed with 8 bags of pears. In P(G>1.5C+5.0)P(G > 1.5C + 5.0)P(G>1.5C+5.0), C C\,C is the mass of a different, independently selected crate. Assume the crate and bag masses are independent.
Calculate P(G>1.5C+5.0)P(G > 1.5C + 5.0)P(G>1.5C+5.0)
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.