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.
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.