The volume of liquid in a particular type of specialty coffee pod, V mlV\text{ ml}V ml, is modeled by a normal distribution with a mean of 230 ml230\text{ ml}230 ml and a standard deviation of 12 ml12\text{ ml}12 ml.
Determine the probability that a randomly selected coffee pod contains less than 215 ml215\text{ ml}215 ml of liquid.
The manufacturer classifies the pods into three categories based on volume: 'Mini', 'Classic', and 'Grande', such that exactly one-third of the total production falls into each category.
Find the volume limits that define the 'Classic' category.
A pod is selected at random from the 'Mini' category.
Calculate the probability that this pod contains more than 220 ml220\text{ ml}220 ml of liquid.
A customer purchases a trial pack consisting of 3 pods chosen at random from the manufacturer's total production.
Find the probability that the pack contains exactly one pod from each of the three categories.
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.