This looks like a normal distribution bell-curve with μ (mean)=0 and σ (standard deviation)=1.
Z is usually calculated from Z=(X-μ)/σ=X in this case. So Z<-2 is equivalent to a datum X=-2.
Normal distribution tables give the probability associated with Z-scores (the area underneath the bell-curve to the left of the Z-score). Z=-2 means 2 standard deviations below the mean.
P[Z<-2]=0.02275 or 2.275%;
P[Z<0]=0.5 or 50% (half the results (area) are below 0 and half above), so:
P[-2<Z<0]=P[Z<0]-P[Z<-2]=0.5-0.02275=0.47725 or 47.725%;
P[Z>2]=P[Z<-2]=0.02275 because of symmetry: the area above Z=2 is the same size as the area below Z=-2;
P[Z<2]=1-0.02275=0.97725 because the area under the bell-curve is 1 (100% probability).