In order to estimate the portion of grades between 66 and 90, first let's find the z-score for these two values, using the formula:
[tex]z=\frac{x-m}{g}[/tex]So we have:
[tex]\begin{gathered} z_1=\frac{66-78}{8}=-1.5 \\ z_2_{}=\frac{90-78}{8}=1.5 \end{gathered}[/tex]Looking at the z-table, a z-score of 1.5 corresponds to a z-value of 0.0668.
Since we have this z-value from the left and right, the percentage we want is:
[tex]\begin{gathered} P=1-0.0668-0.0668 \\ P=0.8664=86.64\text{\%} \end{gathered}[/tex]