The independent random variables CCC and DDD represent the volumes, in millilitres, of coffee dispensed by 'Classic' and 'Deluxe' pods respectively, where
C∼N(45,1.22)andD∼N(60,1.62) C \sim \mathrm{N}(45, 1.2^2) \quad \text{and} \quad D \sim \mathrm{N}(60, 1.6^2) C∼N(45,1.22)andD∼N(60,1.62)The random variables C1,C2C_1, C_2C1,C2 are independent and each has the same distribution as CCC. The random variables D1,D2,D3D_1, D_2, D_3D1,D2,D3 are independent and each has the same distribution as DDD.
Given that the random variable MMM is defined as
M=C1+C2+D1+D2+D35 M = \frac{C_1 + C_2 + D_1 + D_2 + D_3}{5} M=5C1+C2+D1+D2+D3find P(M<52.5)P(M < 52.5)P(M<52.5).
The random variable VVV represents the volume dispensed by a 'Value' pod, such that V∼N(μ,3.52)V \sim \mathrm{N}(\mu, 3.5^2)V∼N(μ,3.52).
Given that P(V−C<8)=0.12P(V - C < 8) = 0.12P(V−C<8)=0.12 and that VVV and CCC are independent,
find the value of μ\muμ, giving your answer to 3 significant figures.
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.