Question

4. Choose any GRE score between 200 and 800. Be creative, choosingunusual scores such as 483. This will allow you to likely not choose a scorethat a fellow student has already selected. Using your chosen score, howmany standard deviations from the mean is your score? (This value is calledthe z-value). Using the table above (or the z table also located in CourseResources), what percentage of students will likely get a score below thisvalue?Let’s use the number 660

Answer 1

Using the z-score formula, get the z-value of the score 660.

$z=\frac{x-\mu}{\sigma}$$\begin{gathered} \text{Substitute} \\ x=660 \\ \mu=500 \\ \sigma=75 \\ \\ z=\frac{x-\mu}{\sigma} \\ z=\frac{660-500}{75} \\ z=\frac{160}{75} \\ z=2.13 \end{gathered}$

The score 660 is 2.13 standard deviation from the mean.

The percentage of students that will likely get a score of 660 is

$\begin{gathered} P(z<2.13)=0.9834 \\ \\ \text{Convert }0.9834\text{ to percentage} \\ 0.9834\rightarrow98.34\% \end{gathered}$

The percentage of students that will likely get a score below 660 is 98.34%.