Chapter 3, Problem 17CR

To determine

To calculate: To convert the score to a scale of 0-100.

Answer to Problem 17CR

The correct option is c .

Explanation of Solution

Given information:The score of the student on a scale of 200-800 is 684.

Formula used: $\text{Proportion}=\frac{\text{Part}}{\text{Whole}}$

Calculation: The score scale ranges from 200-800. First make the lower end of the score as 0.

This can be done by shifting all the scores 200 left. Then, the score range becomes,

  $\begin{array}{l}200-200\text{ to 800-200}\\ \text{ 0 to 600}\end{array}$

And, the obtained score becomes,

  $684-200=484$

Thus, the score of the student on a scale of 200-800 is 684 can be expressed on a scale of 0-600 as 484. That is,

  $\text{Proportion}=\frac{484}{600}$   ...... (1)

Since, we need to obtain the score in the range 0-100, assume the part be x and whole will be 100. That is,

  $\text{Proportion}=\frac{x}{100}$   ...... (2)

Equate equations (1) and (2) to obtain the value of x,

  $\begin{array}{c}\frac{x}{100}=\frac{484}{600}\\ x=\frac{484}{6}\\ =80\frac{4}{6}\\ =80\frac{2}{3}\end{array}$

Hence, the required score on a scale of 0-100 is $80\frac{2}{3}$ .