Ashley is working for the Olympic committee that is trying to determine which athletes to train
by providing coaching and funding to those who may be future Olympians. Unfortunately,
Ashley does not have funding to train all of the interested athletes, so she must first perform a
battery of tests to determine which athletes are the highest ranking—these are the athletes (top 2.5
percent) who will receive funding and coaching. The results from her tests indicate that the mean
on the battery of tests was 80 and the standard deviation was 5. Based on this information, answer
the questions below.
(A) Create a normal distribution that represents the athletes’ scores (go out three standard
deviations on either side of the mean).
(B) Ethan, one of the athletes, received a score of 90.
• What is his percentile rank, and what does this mean?
• What is Ethan’s z-score on the battery of tests, and what does this mean?
• Will Ethan receive funding form Ashley’s committee? Explain why or why not.
(C) Interpret the results of Ashley’s test.
• Where will the measures of central tendency fall on this graph?
• If Ashley were dealing with only the “best of the best” and most of these athletes
performed extremely well with only a few performing poorly, what type of
distribution could Ashley expect?