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.
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.