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 A Level Maths 2.4 Statistical Distributions, covering 2.4.1 Discrete probability distributions, 2.4.2 Binomial distribution as a model, 2.4.3 Calculating binomial probabilities, 2.4.4 Mean and variance of the binomial (A-level only), 2.4.5 Normal distribution as a model (A-level only), 2.4.6 Probabilities using the normal distribution (A-level only), 2.4.7 Links to histograms, mean and standard deviation (A-level only), and 2.4.8 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.