The masses of boxes of apples, A A\,A kg, are distributed such that A∼N(1.5,0.042)A \sim \text{N}(1.5, 0.04^2)A∼N(1.5,0.042).
Four boxes of apples are selected at random.
Calculate the probability that their total mass is less than 5.9 kg.
The masses of bags of pears, P P\,P kg, are such that P∼N(0.8,0.052)P \sim \text{N}(0.8, 0.05^2)P∼N(0.8,0.052).
Two bags of pears are selected at random.
Calculate the probability that the magnitude of the difference in their masses is more than 0.06 kg.
The masses of shipping crates, C C\,C kg, are such that C∼N(4.0,0.08)C \sim \text{N}(4.0, 0.08)C∼N(4.0,0.08).
The random variable G G\,G represents the total mass, in kg, of a single crate packed with 8 bags of pears. In P(G>1.5C+5.0)P(G > 1.5C + 5.0)P(G>1.5C+5.0), C C\,C is the mass of a different, independently selected crate. Assume the crate and bag masses are independent.
Calculate P(G>1.5C+5.0)P(G > 1.5C + 5.0)P(G>1.5C+5.0)
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.