Question

The current Men’s high school track record for the mile is 3:53, set by Alan Webb back in 2006. The average mile time for a high school senior is 4:22 (262 seconds), with a standard deviation of 6.3 seconds. Paul, a high school senior, runs the mile in 4:19 (259 seconds).  

1.) What is Paul’s percentile ranking among high school seniors? HINT: don’t forget that in this case less is better so you will need to reverse the scale!

2.) If Brian’s percentile ranking for running the mile is 72%, what is his mile time?

Answer 1

Mean mile time = 262 seconds, S.D = 6.3 seconds

a)

Paul's run time = 259 seconds

Here, we need to calculate the z-score.

o = Z n - X

z = (259 - 262) / 6.3 = -3 / 6.3 = -0.48

which gives a value of 0.3156 in the z-table.

We need to reverse it as less is better here. We can subtract it with 1.

= 1 - 0.32 = 0.68

The percentile rank is 68.

b)

If the percentile ranking is 72, the z-score is 0.59.

The score will be 0.59 standard deviation less than the mean as less is better here.

Score = mean - 0.59*S.D = 262 - (0.59 * 6.3) = 262 - 3.7 = 258.3 seconds