A shipping facility handles two types of cargo boxes: Premium, PPP, and Economy, EEE. The masses, in grams, of Premium boxes are distributed as P∼N(850,302)P \sim \text{N}(850, 30^2)P∼N(850,302) and Economy boxes are distributed as E∼N(600,252)E \sim \text{N}(600, 25^2)E∼N(600,252).
A Premium box and an Economy box are selected at random.
Find the probability that the mass of the Premium box is less than 140% of the mass of the Economy box.
Two Premium boxes are chosen at random.
Find the probability that their masses differ by more than 45 g.
The facility ships boxes on heavy-duty pallets. Each pallet contains either 6 Premium boxes or 8 Economy boxes. The mass of an empty pallet, WWW, is distributed as W∼N(2000,1002)W \sim \text{N}(2000, 100^2)W∼N(2000,1002).
Find the probability that a pallet of 8 Economy boxes has a greater total mass than a pallet of 6 Premium boxes.
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.