Mathematics Probability & Statistics 2 9709: Linear Combination Of Random Variables Topical Past Paper Questions

The volumes of regular and large coffees at a certain café have independent normal distributions. The mean and standard deviation of the volumes of regular coffees are $ 215 \, cm^{3} $ and $ 2.8 \, cm^{3} $ respectively. The mean and standard deviation of the volumes of large co…

The masses, in kg, of large and small bags of tomatoes have the distributions $ L \sim \mathrm{N}(2.10, 0.12) $ and $ S \sim \mathrm{N}(1.51, 0.09) $ respectively. [5] The price of tomatoes is $4.30 per kg. (b) A large bag of tomatoes and a small bag of tomatoes are chosen at ran…

Each year a transport firm uses X litres of gasoline and Y litres of diesel fuel, where X and Y have the independent distributions $ X \sim \mathrm{N}(10\,700, 950^2) $ and $ Y \sim \mathrm{N}(13\,400, 1210^2) $. (a) Find the probability that in a randomly chosen year the firm us…