Answer :
Final answer:
To figure out how many standard deviations above the mean the player's height is, the z-score formula is used. By substituting the average height and the player's height, and making an educated estimate of the standard deviation, it's found the player's height is approximately 1.31 standard deviations above the mean height.
Explanation:
To determine how many standard deviations above the mean a player's height is, you would use the z-score formula. In this scenario, we lack the standard deviation for the height of soccer players, but what we can infer from the given information and the context, we can approximate that standard deviation might be close to 3 inches (7.62 cm) (a common estimate used in height studies).
The z-score formula is Z = (X - μ) / σ where X is the value of interest (player's height), μ is the mean height, and σ is the standard deviation. This means, you subtract the mean from the value of interest, and then divide that by the standard deviation.
Converting 3 inches into cm we get approximately 7.62 cm. So, if we use this as our standard deviation, we get Z = (182-172) / 7.62 = ~1.31. This implies that the player's height of 182 cm is approximately 1.31 standard deviations above the mean height.
Learn more about standard deviations here:
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