The random variable MMM, representing the final mass of a specialty alloy piece in grams, is defined by the relation
M=5G+2S−3L M = 5G + 2S - 3L M=5G+2S−3Lwhere GGG, SSS, and LLL are independent random variables representing the masses of gold, silver, and the mass lost during smelting respectively, with
G∼N(15,0.82)S∼N(25,1.22)L∼N(10,0.52) G \sim \mathrm{N}(15, 0.8^2) \quad S \sim \mathrm{N}(25, 1.2^2) \quad L \sim \mathrm{N}(10, 0.5^2) G∼N(15,0.82)S∼N(25,1.22)L∼N(10,0.52)Find P(M>104.8)P(M > 104.8)P(M>104.8).
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.