I'm teaching the Cambridge specification of S2 for the first time after teaching Edexcel previously. If anyone is able to clarify this for me I'd be very grateful. It is no doubt something simple that I am missing. Worked Example 3.9 on page 63 of the Cambridge Probability and Statistics 2 book: “A gift package contains a set of three bars of soap. The mass, in grams, of each bar of soap is given by S~N(50,4^2) and the packaging by T~N(90,5^2). The gift package can be posted at a cheap rate if the mass is under 250g. Assuming that S and T are independent, find the probability that a randomly chosen gift package can be posted at the cheap rate.” Ok so the worked examples gives Var(3S+T) as 3^2*4^2 + 5^2. Fine. From the June 2016 CIE S2 Exam paper Q7 (i): “Bags of sugar are packed in boxes, each box containing 20 bags. The masses of the boxes, when empty, are normally distributed with mean 0.4kg and standard deviation 0.01kg The masses of the bags are normally distributed with mean 1.02kg and standard deviation 0.03kg. (i) Find the probability that the total mass of a full box of 20 bags is less than 20.6kg." To me this looks like the same type of question as the worked example from the book and I thought it would be Var(20 Bags + 1 box) = 20^2*0.03^2+0.01^2 But the marking scheme gives the variance as 20*0.03^2+0.01^2. My question is, how are these two questions different and how do I know if I should be squaring the coefficient or not? Thanks so much to anyone who takes the time to read this and help me out.