In order to have grade A, the score needs to be in the top 9%.
Since the scores are normally distributed, the top 9% scores correspond to 91% of the area under the normal curve. That means we need to find a value of z in the z-table that corresponds to the value 0.91 (that is, 91%).
Looking at the z-table, the value of z for a probability of 0.91 is z = 1.34.
Now, to find the score that this value of z represents, we can use the formula below:
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma}\\ \\ 1.34=\frac{x-67.2}{8.5}\\ \\ x-67.2=11.39\\ \\ x=11.39+67.2\\ \\ x=78.59 \end{gathered}[/tex]
Rounding to the nearest whole number, the minimum score for grade A is 79.
