In 2005, the mean number of wins for baseball teams in the American league was 8
ID: 3051776 • Letter: I
Question
In 2005, the mean number of wins for baseball teams in the American league was 81.71 with a standard deviation of 13.07. Because all teams were included, these are population parameters. The Red Sox won 95 games. What is their z-score?
In 2005, the mean number of wins for football teams in the American Football Conference was 8.131 with a standard deviation of 3.70. The Redskins won 10 games. What is their z-score?
Which team did better?
How many games with the lower z-score have had to win to beat the team with the higher z-score?
Explanation / Answer
Z score = (X - mean)/standard deviation)
Z score of Red Sox = (95 - 81.71)/13.07
= 1.02
Z score of Redskins = (10-8.131)/3.70
= 0.51
So, the Red Sox did better (higher z score)
Redskins must have an Z score above 1.02
Let X be the number of games Redskins must win to beat Red Sox
(X - 8.131)/3.70 = 1.02
X = 11.91
= 12 games
Redskins must win 12 games to beat Red Sox
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