I'm pretty sure that this is correct?
No, these are false...
What you did in a first time was right, except for the red part corrected by Mr F :
Why so ? Because |Z|>1 means "Z<-1 OR Z>1"
Since the event "Z<-1" and the event "Z>1" cannot happen at the same time,
(this is the formula of P(A u B)=P(A)+P(B) when A and B are disjoint)