Regular and large bags of coffee beans are independently filled at a factory.
The weights of coffee in regular bags, RRR, are normally distributed with mean 250 g and standard deviation 6 g.
The weights of coffee in large bags, LLL, are normally distributed with mean 480 g and standard deviation 10 g.
The random variable W W\,W represents the total weight of coffee in 2 randomly selected regular bags minus the weight of coffee in 1 randomly selected large bag.
W∼N(a,b)W \sim \text{N}(a, b)W∼N(a,b) where a a\,a and b b\,b are positive constants.
Find the value of a a\,a and the value of bbb.
Find the probability that a randomly chosen large bag contains more than 1.9 times the amount of coffee in a randomly chosen regular bag.
A random sample of 3 regular bags is taken.
Find the probability that the weight of the first regular bag in the sample is at least 4 g more than the mean weight of all 3 regular bags in the sample.
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.