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The average score on the SAT Mathematics test is $500$. Eleanor received a $680$ on the SAT Mathematics test. The SAT Mathematics test has a standard deviation of $100$. Gerald received a $27$on the ACT Mathematics test. The average ACT Mathematics test score is $18$ points. The ACT Mathematics exam score has a standard deviation of $6$ points.

The inflection points are the points where the curve shifts from being concave up to being concave down. These inflection points are always one standard deviation distant from the mean on a normal density curve.

Eis's standardized score is shown below.

$$\begin{gathered} z\left(Eleanor\right)=\frac{x鈭�渭}{蟽} \\ =\frac{680鈭�500}{100} \\ =1.80 \end{gathered}$$

The standardized score for G can be found in the table below.

$$\begin{gathered} z\left(Gerald\right)=\frac{x鈭�渭}{蟽} \\ =\frac{27鈭�18}{6} \\ =1.50 \end{gathered}$$

E's score of $680$was $1.80$standard deviations higher than the mean, whereas G's score of$27$was $1.50$standard deviations higher. Therefore, the standardized score for Eis $180$ and the standardized score for G is $150$