Question

a. For runners in a race, a low time means a faster run. The winners in a race have the shortest running times. Is it more desirable to have a finish time with a high or a low percentile when running a race?

b. The $20th$ percentile of run times in a particular race is $5.2$ minutes. Write a sentence interpreting the $20th$ percentile in the context of the situation.

c. A bicyclist in the$90th$ percentile of a bicycle race completed the race in $1$ hour and $12$ minutes. Is he among the fastest or slowest cyclists in the race? Write a sentence interpreting the $90th$ percentile in the context of the situation.

Short answer

a. It is desirable to finish with low percentile.

b. It can be interpreted as $20\%$of numbers finished their race in $5.2$minutes or less.

c. The $90\%$cyclist are fastest than $10\%$in the race.

Step-by-step solution

Content Introduction

The frequency of a data value is the number of times it happens.

Explanation (Part a)

It is desirable to finish with low percentile because low percentile means a short time.

Explanation (Part b)

It can be interpreted as $20\%$ of numbers finished their race in $5.2$minutes or less.

Explanation (Part c)

It can be interpreted as the $90\%$bicyclist finished their race in $1hour12min$or less. Only$10\%$bicyclist completed their race with time.The $90\%$ cyclist are fastest than $10\%$in the race.