Chapter 12.4, Problem 19PPE

To determine

To find: The possible scores for the percentile rank of $80$ .

Explanation of Solution

Given information:

The scores of other finalists at a science fair are $87,89,81,85,87,83,86,94,90,97,80,89,85,\text{ and 88}$ . There are $15$ finalist including me. Percentile rank of my score is $80$ .

Calculation:

A percentile rank of a data value is the percentage of data values that are less than and equal to that value.

Arranging the scores in ascending order −

  $80,81,83,85,85,86,87,87,88,89,89,90,94,97$ .

Since the percentile rank of my score is $80$ out of $15$ scores. This means my score should be at $12$ th position if arranged in ascending order.

Therefore, $\text{My score}\ge \text{89}$ .

Also $80\%$ of scored should be less than or equal to my score.