Question

when a team loses possession of the ball to the opposing team before a player takes a shot at their team's basket. Turnovers are undesirable in many sports, not just basketball, and sometimes end up costing a team the game. Sports analysts use a calculated variable called turnover percentage (TOP) to measure the percentage of a player's scoring attempts in a season that result in a turnover. Analysts report this TOP value for each player in the professional NBA and WNBA leagues each season. The distribution of these TOP values is generally mound-shaped and symmetric. In a recent year, the mean TOP for players in the men's National Basketball Association (NBA) was 15.43 with a standard deviation of 3.93. That same year, the mean TOP for players in the women's National Basketball Association (WNBA) was 16.56 with a standard deviation of 5.43. Vince and Luda are die-hard basketball fans. In this recent year, Vince's favorite male player in the NBA had a turnover percentage of 9.89, while Luda's favorite female player in the WNBA had a turnover percentage of 8.96. Round all calculated answers to 4 decimal places. 1. What is the z-score for the TOP of Vince's favorite NBA player? z= 2. What is the z-score for the TOP of Luda's favorite WNBA player? value for each player in the professional NBA and WNBA leagues each season. The distribution of these TOP values is generally mound-shaped and symmetric. In a recent year, the mean TOP for players in the men's National Basketball Association (NBA) was 15.43 with a standard deviation of 3.93. That same year, the mean TOP for players in the women's National Basketball Association (WNBA) was 16.56 with a standard deviation of 5.43. Vince and Luda are die-hard basketball fans. In this recent year, Vince's favorite male player in the NBA had a turnover percentage of 9.89, while Luda's favorite female player in the WNBA had a turnover percentage of 8.96. Round all calculated answers to 4 decimal places. 1. What is the z-score for the TOP of Vince's favorite NBA player? z= 2. What is the z-score for the TOP of Luda's favorite WNBA player? z= 3. Based on the z-scores, whose favorite player had a better turnover percentage, relative to the other players in the league in the year they played? A. Vince's B. Luda's C. The players performed equally well

Answer 1

1. The z-score for the turnover percentage (TOP) of Vince's favorite NBA player is
`\( \text{z} = -1.6367 \).`

2. The z-score for the TOP of Luda's favorite WNBA player is
`\( \text{z} = -1.0740 \).`

3. Based on the z-scores, Luda's favorite WNBA player had a better turnover percentage relative to other players in the league in the year they played.

Step-by-step explanation:

The z-score is calculated using the formula
`\( \text{z} = \frac{\text{X} - \text{Mean}}{\text{Standard Deviation}} \).`

1. For Vince's favorite NBA player:

`\( \text{z} = (9.89 - 15.43)/(3.93) \)`

`\( \text{z} = -1.6367 \)`

2. For Luda's favorite WNBA player:

`\( \text{z} = (8.96 - 16.56)/(5.43) \)`

`\( \text{z} = -1.0740 \)`

The negative z-scores indicate that both players' turnover percentages are below the mean, suggesting they performed better than the average player in terms of turnovers.

A lower (less negative) z-score implies a better performance relative to the league. Comparing the z-scores, Luda's favorite WNBA player has a higher (less negative) z-score, indicating a better turnover percentage compared to Vince's favorite NBA player in the respective leagues.

Therefore, based on z-scores, Luda's favorite player had a better turnover percentage relative to other players in the league in the year they played.