Answer:
The minimum (cut off) score you need to receive this award is;
[tex]722.2[/tex]Explanation:
Given that the top 3% of the students receive a $500 prize.
[tex]P=1-0.03=0.97[/tex]We will then find the z-score that corresponds to the given probability.
[tex]z=1.88[/tex]Recall that;
[tex]z=\frac{X-\mu}{\sigma}[/tex]Given;
[tex]\begin{gathered} \mu=553 \\ \sigma=90 \end{gathered}[/tex]substituting the values;
[tex]\begin{gathered} 1.88=\frac{X-553}{90} \\ X-553=1.88\times90 \\ X=553+1.88\times90 \\ X=722.2 \end{gathered}[/tex]Therefore, the minimum (cut off) score you need to receive this award is;
[tex]722.2[/tex]
