Chapter 2, Problem T2.10SPT

To determine

To find: that which one is better on the exam.

Answer to Problem T2.10SPT

Gina-Her standardized score is higher than Colleen’s

Explanation of Solution

Given:

  $\begin{array}{c}{\mu }_G=470\\ {\sigma }_G=110\\ x_G=500\end{array}$

  $\begin{array}{c}{\mu }_C=510\\ {\sigma }_C=103\\ x_C=530\end{array}$

Formula used:

  $z=\frac{x-\mu }{\sigma }$

Calculation:

  $\begin{array}{c}{z}_G=\frac{x-\mu }{\sigma }\\ =\frac{500-470}{110}\\ =0.27\end{array}$

  $\begin{array}{c}{z}_C=\frac{x-\mu }{\sigma }\\ =\frac{530-510}{103}\\ =0.19\end{array}$

It is observed that $z_G>z_C$ which implies that which has highest z-score that will be better on SAT exam relative to the year in which they took exam.

Hence, the correct option is (c)