First, find the z-score of 92 using the formula
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ \\ \text{Substitute the following} \\ x=92 \\ \mu=84.28 \\ \sigma=6.71 \end{gathered}[/tex][tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ z=\frac{92-84.28}{6.71} \\ z=\frac{7.72}{6.71} \\ z=1.15 \end{gathered}[/tex]Look for the value of z-score in the z-table
Since we are looking for percentage of higher than 92, subtract 0.87493 from 1
[tex]\begin{gathered} P(Z>1.15)=1-0.87493 \\ P(Z>1.15)=0.12507 \end{gathered}[/tex]Multiply the result by 100% to get the percentage.
[tex]0.12507\cdot100\%=12.507\%[/tex]Therefore, the percentage of students who scored higher than you on the exam is 12.507%.
