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Answer:
It is better for the warriors to use man-to-man defense.
Step-by-step explanation:
The complete question is: The Westwood Warriors basketball team wants to score more points. To get better at scoring points the team is trying to improve its offensive strategies. Some opponents primarily use a zone defense, while others primarily use a man-to-man defense. When the Warriors play against teams that use a zone defense they score an average of 67 points per game with a standard deviation of 8 points per game. When they play against teams that use a man-to-man defense they score an average of 62 points per game with a standard deviation of 5 points per game.
Since the Warriors started using their improved offensive strategies they have played two games with the following results.
Against the McNeil Mavericks
Maverick defense: zone
Warrior points: 77
Against the Round Rock Dragons
Dragon defense: man-to-man
Warrior points: 71
What is the Z-score of these values?
We are given that when the Warriors play against teams that use a zone defense they score an average of 67 points per game with a standard deviation of 8 points per game. When they play against teams that use a man-to-man defense they score an average of 62 points per game with a standard deviation of 5 points per game.
We have to find the z-scores.
- Finding the z-score for the zone defense;
Let X = <u><em>points score by warriors when they use zone defense</em></u>
The z-score probability distribution for the normal distribution is given by;
Z = ~ N(0,1)
where, = mean score = 67 points
= standard deviation = 8 points
It is stated that the Warriors scored 77 points when they used zone defense, so;
z-score for 77 =
= = <u>1.25</u>
- Finding the z-score for the zone defense;
Let X = <u><em>points score by warriors when they use man-to-man defense</em></u>
The z-score probability distribution for the normal distribution is given by;
Z = ~ N(0,1)
where, = mean score = 62 points
= standard deviation = 5 points
It is stated that the Warriors scored 71 points when they used man-to-man defense, so;
z-score for 71 =
= = <u>1.8</u>
<u></u>
So, it is better for the warriors to use man-to-man defense.