AP Statistics 1.9: Calculating Z-Scores

Calculate a z-score from a value, population mean, and standard deviation, then interpret its signed distance from the mean in context.

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, as shown in the table below.

Table for Question 1.9.D—Calculate z-scores with population parameters question 1 — AP Statistics

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

Part (b):
The z-score for a player who can lift a weight of 370 pounds is $z=\frac{370-310}{25}=2.4$ . The z-score indicates that the amount of weight the player can lift is 2.4 standard deviations above the mean for all previous players in this position.

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1.9.D—Calculate z-scores with population parameters question 1