1) We need to work out two Z-scores, one for the lower number and one for the higher.
Z1=(47-53)/6=-1; Z2=(65-53)/6=2.
N(-1)=1-N(1)=1-0.8413=0.1587; N(2)=0.9772.
The probability is 0.9772-0.1587=0.8185 (closest answer option 81.5%).
2) Z1=(41-53)/6=-2; Z2=(47-53)/6=-1.
N(-2)=1-N(-2)=1-0.9772=0.0228; N(-1)=0.1587.
The probability is 0.1587-0.0228=0.1359 (closest answer option 13.5%).
3) Z=(59-53)/6=1, N(X<59)=0.8413⇒N(X>59)=1-0.8413=0.1587 (~16%).
4) <65? Z=2, N(2)=0.9772 (see Z2 in part (1).) About 97.5%.