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.
390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.