Statistical Problem (part 2) Following my question I found another problem. Having the same data from the other question: > There are 2 melon stores. The melon weights follow a normal distribution. > > * Store A -> μ = 2.1Kg, σ = 0.7Kg; > * Store B -> μ = 2.5Kg, σ = 0.2Kg; > But now what I can't figure out is: > If I buy 6 melons from each store, what is the probability of the sum of the weight of the melons from **A** being greater than the sum of the weight of the melons from the store **B**. I'm really, really rusty at this stuff, and my exame is in a week... So far I have that μA = 6*2.1 and σA = sqrt(6*0.7^2) and μB = 6*2.5 and σB = sqrt(6*0.2^2) Thank you guys.

So if we call $W_A$ the weight of 6 melons from store $A$, and $W_B$ the weight of 6 melons from store $B$, you are interested in the distribution of $W_A-W_B$. In particular, we want to find $P(W_A-W_B>0)$. We know the sum of two Gaussians is a Gaussian, so how does the difference of two Gaussians behave? Well, try to write down the distribution of $-W_B$. If you are still stuck, give a shout.