If Santiago finished in 51st place among the men, with a time of 20.9 minutes. Santiago’s percentile is 22.2 and Keisha’s percentile is 32.6.
What is the percentile?
Santiago’s percentile is:
Percentile =50/225
Percentile = 22.2
z-score is:
z-score = (20.9 – 24.758)/5.026
z-score = –0.77
Keisha’s percentile is:
Percentile = 32/98
Percentile = 32.6
z-score:
z-score = (25.2 – 28.891)/6.481
z-score = –0.57.
Therefore since lower finish times are better Santiago tend to have a better finish among men than Keisha had among women.
The complete question is:
Scenario 2-5
Ninety-eight women and 225 men participated in a five kilometer road race. Below are summary statistics
from Minitab on their times in the race.
Descriptive Statistics: Women, Men
Variable N Mean StDev Minimum Q1 Median Q3 Maximum
Women 98 28.891 6.481 17.717 24.229 26.917 32.525 48.800
Men 225 24.758 5.026 15.050 21.117 24.050 27.608 48.417
Use Scenario 2-5. Santiago finished in 51st place among the men, with a time of 20.9 minutes. Keisha
finished 33rd among women, with a time of 25.2 minutes. Use percentiles and z-scores to compare Santiago’s and Keisha’s relative standing among men and women, respectively