posted by Shellie on .
Assume that the points scored by the winning teams for all NCAA games follow a bell-shaped distribution. Using the mean of 76.5 and the standard deviation of 7, estimate the percentage of all NCAA games in which the winning team scores 84 or more points. 90 points. The winning scores are as follows: 90, 85, 75, 78,71, 65, 72, 76, 77, 76. The answers are 16% and 2.5% I have tried to solve the problem by determining the z score (84-76.5/7 = 1.072) and then use chebyshev's theorem (1 - 1 / 1.072^2 = .13) this is not quite right....what am I missing? I see that only 2 teams scored 84 points or higher and only 1 scored 90 or higher. I would follow the same equations as above for 90.
Look up Z score in table in back of statistics text labeled something like "areas under normal distribution" for calculated Z scores. The colummn for the smaller area should give the proportion you desire. Convert to precentage.
I hope this helps. Thanks for asking.