We have to find the z-score at first, then use it to find the percentage of 70 or higher
The rule of the z-score is
[tex]z=\frac{x-\mu}{\sigma}[/tex]
μ is the mean
σ is the standard deviation
Since the average score is 75, then
[tex]\mu=75[/tex]
Since the standard deviation is 10, then
[tex]\sigma=10[/tex]
Since we need the percentage of 70, then
[tex]x=70[/tex]
Substitute them in the rule above to find z
[tex]\begin{gathered} z=\frac{70-75}{10} \\ z=-\frac{5}{10} \\ z=-0.5 \end{gathered}[/tex]
Now, we will search in the table for the value of -0.5
The value of -0.5 is 0.30854
Since we need the percentage of 70 or higher, then
[tex]\begin{gathered} P(x\ge70)=1-P(x) \\ P(x\ge70)=1-0.30854 \\ P(x\ge70)=0.69146 \end{gathered}[/tex]
Change it to percent
[tex]\begin{gathered} P(x\ge70)=0.69146\times100\text{ \%} \\ P(x\ge70)=69.146\text{ \%} \end{gathered}[/tex]
The percentage of 70 or higher is about 69.15%
