The volume of coffee, VVV ml, dispensed by an automated brewing machine is normally distributed with a mean of 340 ml and a standard deviation of 15 ml. Servings containing more than 365 ml are categorized as 'Premium' servings.
Determine the proportion of servings categorized as 'Premium'.
The manufacturer wants to award a 'Standard' quality mark to the servings in the top 90%, which are those containing at least kkk ml. Find the value of kkk.
Within the 'Premium' category, the largest 15\frac{1}{5}51 of servings are further designated as 'Gold Reserve'. Find the minimum volume, sss, required for a 'Gold Reserve' designation.
A quality control officer randomly selects 5 servings that were already categorized as 'Premium'. Find the exact probability that at least one of these is a 'Gold Reserve' serving.
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.