Q. 29 - Elementary Statistics

Question

Verbal GRE Scores. Refer to Problem 28, and fill in the following blanks.

a. Approximately $68\%$of students who took the verbal portion of the GRE scored between_______and________

b. Approximately $95\%$ of students who took the verbal portion of the GRE scored between_______and________

c. Approximately $99.7\%$of students who took the verbal portion of the GRE scored

between_______and________ 

Step-by-Step Solution

Answer

a. Approximately $68\%$of students who took the verbal portion of the GRE scored between$141.25 points$ and $158.75 points$.

b. Approximately $95\%$of students who took the verbal portion of the GRE scored between $132.5 points$and $167.5 points.$

c. Approximately $97\%$of students who took the verbal portion of the GRE scored

between $123.75 points$ and $176.25 points.$

Part (a) Step 1: Given Information

The scores on the verbal portion of GRE are approximately normal with mean $\left(\mu \right)=150$points and standard deviation $\left(\sigma \right)=8.75$ points.

Part (a) Step 2: Explanation

Computation:

Applying the proper empirical rule, moreover$68\%$ of values lie in the interval $(\mu -\sigma ,\mu +\sigma )$

$\begin{array}{c}(\mu -\sigma ,\mu +\sigma )=(150-8.75,150+8.75)\\ =(141.25,158.75)\end{array}$

About $68\%$ of students who took the verbal section of the GRE scored between $141.25$ and $158.75$ points on this part of the test.

Part (b) Step 1: Given Information

The verbal section of the GRE results are roughly normal, with a mean $\mu$ of $150$ points and a standard deviation $\sigma$ of $8.75$ points

Part (b) Step 2: Explanation

Applying the proper empirical rule, moreover$95\%$ of values lie in the interval $(\mu -2\sigma ,\mu +2\sigma )$

$\begin{array}{c}(\mu -2\sigma ,\mu +2\sigma )=(150-17.5,150+17.5)\\ =(132.5,167.5)\end{array}$

As a result, over $68$ percent of students who took the GRE verbal section scored between $132.5$and $167.5$ points.

Part (c) Step 1: Given Information

The scores on the verbal portion of GRE are approximately normal with mean $\left(\mu \right)=150$points and standard deviation $\left(\sigma \right)=8.75$ points.

Part (c) Step 2: Explanation

Applying the proper empirical rule, moreover$99.7\%$ of values lie in the interval $(\mu -3\sigma ,\mu +3\sigma )$

$(\mu -3\sigma ,\mu +3\sigma )=(150-26.25,150+26.25)$

$=(123.75,176.25)$

As a result, over $68$ percent of students who took the GRE verbal section scored between $123.75$ and $176.25$points.