standard deviation of 62 points. For each league, the dist shaped. (a) Find the z-scores of Lena's total points scored last season as a player in Shoreline Youth. Center and Martina's total points scored last season as a player in Town Sports Club. Round. your answers to two decimal places. z-score of Lena's total points scored last season: z-score of Martina's total points scored last season: (b) Relative to her population, who was the lower scorer? Choose the best answer based on the z-scores of the two players. O Lena O Martina O It is unclear who was the lower scorer relative to her population X

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**Basketball Statistics: Analyzing Player Performance Using Z-Scores**

Shoreline Youth Center and Town Sports Club are two local youth basketball leagues. Last season, Lena scored a total of 438 points in Shoreline Youth Center, and Martina scored a total of 541 points in Town Sports Club.

Last season, the total points scored per player in Shoreline Youth Center had a population mean of 369 points and a standard deviation of 48 points. The total points scored per player in Town Sports Club had a population mean of 405 points and a standard deviation of 62 points. For each league, the distribution of total points scored last season per player was clearly bell-shaped.

**Tasks**

(a) **Find the Z-Scores**

Calculate the z-scores of Lena's total points and Martina's total points. Round your answers to two decimal places.

- Z-score of Lena's total points scored last season: [ ]
- Z-score of Martina's total points scored last season: [ ]

(b) **Determine the Lower Scorer Relative to Population**

Relative to her population, who was the lower scorer?

Choose the best answer based on the z-scores of the two players:

- Lena
- Martina
- It is unclear who was the lower scorer relative to her population

_[Explanation Button]_

_[Check Button]_

**Legend**: The z-score helps to understand how a specific score compares to the mean of a distribution. It's a measure of how many standard deviations an element is from the mean. In this case, you can compare scores across different distributions (leagues) to see who performed better relative to their peers.
Transcribed Image Text:**Basketball Statistics: Analyzing Player Performance Using Z-Scores** Shoreline Youth Center and Town Sports Club are two local youth basketball leagues. Last season, Lena scored a total of 438 points in Shoreline Youth Center, and Martina scored a total of 541 points in Town Sports Club. Last season, the total points scored per player in Shoreline Youth Center had a population mean of 369 points and a standard deviation of 48 points. The total points scored per player in Town Sports Club had a population mean of 405 points and a standard deviation of 62 points. For each league, the distribution of total points scored last season per player was clearly bell-shaped. **Tasks** (a) **Find the Z-Scores** Calculate the z-scores of Lena's total points and Martina's total points. Round your answers to two decimal places. - Z-score of Lena's total points scored last season: [ ] - Z-score of Martina's total points scored last season: [ ] (b) **Determine the Lower Scorer Relative to Population** Relative to her population, who was the lower scorer? Choose the best answer based on the z-scores of the two players: - Lena - Martina - It is unclear who was the lower scorer relative to her population _[Explanation Button]_ _[Check Button]_ **Legend**: The z-score helps to understand how a specific score compares to the mean of a distribution. It's a measure of how many standard deviations an element is from the mean. In this case, you can compare scores across different distributions (leagues) to see who performed better relative to their peers.
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