The Z score for the limits is Z(15.99)=(15.99-16)/0.05=-0.2; Z(16.01-16)/0.05=0.2.
P(0.2)=0.5793, P(-0.02)=1-P(0.2)=0.4207. Therefore P(0.2)-P(-0.2)=2P(0.2)-1=1.1586-1=0.1586.
The probability of the inside diameter being between 15.99 and 16.01 cm is 0.1586 or 15.86%.