Given the information on the problem, we can use the mean and the standard deviation to find the z score:
[tex]\begin{gathered} \mu=14 \\ \sigma=0.6 \\ \Rightarrow z=\frac{12.7-14}{0.6}=-2.16 \end{gathered}[/tex]thus, we have that the probability that the item will be less than 12.7 inches long is:
[tex]P(Z<-2.16)=0.0154[/tex]according to the z-score chart.
Therefore, 1.54% will be shorter than 12.7 inches
