The weight of a large loaf of bread is a normal variable with mean 420g and standard deviation 30g. The weight of a small loaf is a normal variable with mean 220g and standard deviation 10g. 1) Find the probability that 5 large loaves of bread are heavier than 10 small loaves. My Working: Let X be the weight of a large loaf, Y be the weight of a small loaf X~N(420, 900) , Y~N(220,100) 5X>10Y 5X-10Y>0 X-2Y>0 E(X-2Y)=E(X) - 2E(Y)=420-440=-20 Var(X-2Y)=Var(X)+4Var(Y)=900+400=1300 P(X-2Y>0)=P(Z>20/(1300)^1/2)=P(Z>0.5547)=0.2896 But the answer given is totally different. Is there anything I miss in my working?