Use the normal distribution function on your graphing calculator to calculate the percentile that David and Regina fall in.
David: 98th percentile Regina: 97th percentile Faster Person: David is relatively faster.
Practice makes perfect
We are asked to find the percentiles in which two athletes fall. Let's first convert David's and Regina's personal best times into seconds.
David:& 2(60)+2 = 122 seconds
Regina:& 2(60)+10 = 130 seconds
Next we will draw two normal distributions, one showing the standard for boys and another showing the standard for girls. The percentile that David and Regina fall in is the area under the curve that is above their personal bests. Remember: the lower the time, the better.
As we can see, David falls in a higher percentile than Regina. However, for good measure we will calculate these percentiles using the normal distribution function on a graphing calculator.
David
The lower limit of David's personal best of 122. To make sure we cover nearly everything that is to the right of the lower limit, we will enter a very high number for our upper limit. On the calculator push 2nd, then VARS, choose the second option. We are given that for boys' 800-meter freestyle μ= 149 and σ = 13.6.
Having entered all of the values, push ENTER until we get a result.
David is in approximately the 98th percentile of runners.
Regina
Let's repeat this procedure for Regina. Recall that the lower bound for Regina is 130. We are also given that for girls' 200-meter freestyle μ = 145 and σ= 8.2.
Regina is in approximately the 97th percentile of runners.
