For the following homework question, I haven't been able to get an answer, and I haven't been able to figure out my mistake. Was hoping someone could help.
My first thought was that X-Y will be normal with mean- 5-5=0 and variance- (.2)^2 + (.2)^2= 0.08. Then we can simply compute the value (which I got to be .2763). This is not correct according to the answer.
I then realized that we should have 25 sets (for the students). So I ended up using a distribution 25(X-Y) w/ mean- 0 * 25=0 and variance- .08 * 25= 2. We also adjust the bounds, getting P(-2.5<25(X-Y)<2.5). This got me .9229
For part b, I'm guessing we use the central limit theorem (we have >30 iid samples). Am I correct there? Can't verify since my approach for part 1 is wrong.