Assume normal distribution.
Z=(X-m)/s where X is the test value, m=mean=120mm, s=1.5mm.
Z1=(116-120)/1.5=-8/3; Z2=(124-120)/1.5=8/3. These are symmetrical about the mean.
8/3=2.67 approx.
Z1 corresponds to a probability of 0.0038 and Z2=0.9962. Note that Z1+Z2=1 because of symmetry.
Z2-Z1=0.9924 or 99.24% probability that the rod length lies between 116mm and 124mm.
Note that because of symmetry, this probability is 1-2*0.0038=1-0.0076.