Question

Scenario: A professional sports team evaluates potential players for a certain position based on two main characteristics: speed and strength. Strength is measured by the amount of weight lifted, with more weight indicating more desirable (greater) strength. From previous strength data for all players in this position, the amount of weight lifted has a mean of 310 pounds and a standard deviation of 25 pounds.

Calculate and interpret the z-score for a player in this position who can lift a weight of 370 pounds.

Answer 1

Using the z-score formula, a player who can lift 370 pounds has a z-score of 2.4, which means their strength is 2.4 standard deviations above the mean, indicating they are significantly stronger than average.

Step-by-step explanation:

To calculate the z-score for a player who can lift 370 pounds, when the mean weight lifted by players at this position is 310 pounds with a standard deviation of 25 pounds, use the following z-score formula:

z = (X - μ) / σ

Where:

• X is the value to be standardized, which is the player's weight lift of 370 pounds.
• μ (mu) is the mean of the data set, which is 310 pounds.
• σ (sigma) is the standard deviation of the data set, which is 25 pounds.

Thus, the calculation would be:

z = (370 - 310) / 25
z = 60 / 25
z = 2.4

The z-score of 2.4 indicates that this player's strength is 2.4 standard deviations above the mean. This is a relatively high score, suggesting that the player is significantly stronger than the average player in this position.