The amounts of a certain mineral that can be produced in a day from mines $1$, $2$, and $3$ are independent normal random variables with means equal to $80$, $90$, and $75$ pounds, respectively, and with standard deviations equal to $12$, $14$, and $10$ pounds, respectively. On a given day, what is the probability that the combined amount of mineral produced from all three mines exceeds $283$ pounds?
I know this might be a little advanced for me since I am teaching myself this topic. I am going ahead a little to see what certain problems might be like. I think it might be a good idea to see what the working of these certain problems might look like.
From my understanding, we could work with the sum random variable $Y=X_1+X_2+X_3$, where random variable $X_i$ stands for the daily amount of mineral that can be produced from mine $i$
I know we want to find $P(X>283)$.
Can someone help me with this? I am trying this problem for fun and it seems like something good to know for later. I think seeing this problem will help my understanding of this topic when learning it later by myself.