Chapter 2, Problem 10PT

To determine

To find: The person who did better on the exam.

Answer to Problem 10PT

J did better on the exam Therefore option (C) is the right option.

Explanation of Solution

Given:

J scored 500

C scored 530

1. Collen- she scored 30 points higher than Jane.
2. Collen- her standardized score is higher than Jane’s.
3. Jane- her standardized score is higher than Colleen’s.
4. Jane- the standard deviation was bigger in 2009.
5. The two sisters did equally well-their z -scores are the same.

Calculation:

According to the old scale in 1990s, the mean score was $\mu =470$ and the standard deviation was $\sigma =110$ for Math scores. According to the new scale in 2009, the mean score was

  ${\mu }_2=515$ And the standard deviation was ${\sigma }_2=116$ for Math scores.

Also informed that Jane took the SAT in 1994 and scored 500. Her sister Colleen took the SAT in 2009 and scored 530.

By definitions, Jane's standardized score (z-score) is given as follows:

  $\begin{array}{l}z=\frac{x_1-{\mu }_1}{{\sigma }_1}\\ =\frac{500-470}{110}\\ =0.27\end{array}$

By definitions, Colleen's standardized score (z-score) is given as follows:

  $\begin{array}{l}z=\frac{x_1-{\mu }_1}{{\sigma }_1}\\ =\frac{530-515}{116}\\ =0.13\end{array}$

As the Jane's standard score is greater than that of Colleen's, so Jane did better on the exam. Therefore option (C) Jane − her standardized score is higher than Colleen's is the right option.

Conclusion:

Therefore, J did better on the exam Therefore option (C) is the right option.