To find the 70th percentile we look for the z value that gives the following probability:
[tex]P(Z\leq z)=0.70[/tex]Looking at the standard normal distribution table we notice that this probability happens when:
[tex]z=0.5244[/tex]Then we need the z score to be 0.5244 .Now that we know this we use its definition to find the value of x that gives this z score:
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ \frac{x-267}{39}=0.5244 \\ x-267=20.4516 \\ x=267+20.4516 \\ x=287.45 \end{gathered}[/tex]Therefore, the 70th percentile is 287.45
