Question

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 used a new offensive strategy against this defense, they scored 77 points. What is the Z-score of this value

Answer 1

It is better for the warriors to use man-to-man defense.

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 = points score by warriors when they use zone defense

The z-score probability distribution for the normal distribution is given by;

Z =
`(X-\mu)/(\sigma)` ~ N(0,1)

where,
`\mu` = mean score = 67 points

`\sigma` = standard deviation = 8 points

It is stated that the Warriors scored 77 points when they used zone defense, so;

z-score for 77 =
`(X-\mu)/(\sigma)`

=
`(77-67)/(8)` = 1.25

• Finding the z-score for the zone defense;

Let X = points score by warriors when they use man-to-man defense

The z-score probability distribution for the normal distribution is given by;

Z =
`(X-\mu)/(\sigma)` ~ N(0,1)

where,
`\mu` = mean score = 62 points

`\sigma` = 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 =
`(X-\mu)/(\sigma)`

=
`(71-62)/(5)` = 1.8

So, it is better for the warriors to use man-to-man defense.