Chapter 12.4, Problem 21PPE

To determine

To find: The possible height for the replacement player.

Answer to Problem 21PPE

Height of the replacement player should be $\le 73.5$ .

Explanation of Solution

Given information:

The heights(in inches) of the players on a basketball team are $74,79,71.5,81,73,76,78,71,72,73.5$ .

When a $76$ inch tall player is replaced, the percentile rank of $73.5$ inch tall player becomes $60$ .

Calculation:

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

The heights(in inches) of the players on a basketball team are $74,79,71.5,81,73,76,78,71,72,73.5$ .

Arranging the heights in ascending order −

  $\text{71,71}\text{.5,72,73,73}\text{.5,74,76,78,79,81}$ .

Let us assume height of the replacement player is $x$ inch. There are total $10$ player. So, when the $76$ inch tall player is replaced, the percentile rank of $73.5$ inch tall player becomes $60$ , this means the position of $73.5$ inch player becomes 6^th.

  $\text{71,71}\text{.5,}x,\text{72,73,73}\text{.5,74,78,79,81}$ . This is possible only if $x\le 73.5$ .

Hence, height of the replacement player should be $x\le 73.5$ .