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.
