Download Statistical Reasoning in Sports Worksheet#8.5 (p.282-289)

Statistical Reasoning in Sports Worksheet#8.5 (p.282-289)
Name _______________________ Per._____ Date _____________
Use the Normal Distribution, Normal Curve, and Normal Table for
distributions of athletic PERFORMANCES that are approximately
symmetric, unimodal, and bell-shaped
( 1 ) During his football career, running back Emmitt Smith
earned a place as one of the best rushers of all time. Over
the 226 games in his career, his mean rushing yards per
game average was 81.2 yards/game with a standard
deviation of 42.7 yards/game. Also, the distribution of
these 226 values is roughly symmetric, unimodal, and bellshaped.
Emmitt Smith. Photo credit sikids.com
(a) Sketch what this distribution should look like by drawing a bell-shaped curve and labeling the mean,
mean  1 SD, mean  2 SD, and mean  3 SD.
(b) Between which two values would you expect the middle 68% of his PERFORMANCES to be?
(c) What percent of his PERFORMANCES would you expect to be above 123.9 yards?
(d) What percent of his PERFORMANCES would you expect to be below 75 yards?
(e) What percent of his PERFORMANCES would you expect to be between 75 yards and 150 yards?
(f) Calculate and interpret the z-score for his best game: 237 yards. Would you consider this an
exceptional PERFORMANCE? Explain.
More practice exercises:
In the 2014 regular season, each of the 32 NFL teams played 16 games. The distribution of points
scored per team in each game is approximately symmetric, unimodal, and bell-shaped. The mean was
22.6 points with a standard deviation of 5.8 points.
(2) In approximately what percent of games would
you expect one team to score fewer than 28.4
points?
(3) In approximately what percent of games would
you expect one team to score more than 16.8
points?
(4) In approximately what percent of games would
you expect one team to score fewer than 14
points?
(5) In approximately what percent of games would
you expect one team to score between 14 and 22.6
points?
(6) The Green Bay Packers scored 55 points in one
game. What was their z-score for that game?
(7) What would be the z-score for a team that
gets shut out (scores 0 points)?