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Answer :
Final answer:
The z-score of a person who is 59 inches tall, given an average height of 66 inches with a standard deviation of 3.5 inches, is -2.00. This means they are 2 standard deviations below the average height.
Explanation:
A Z-score, also known as a standard score, is a statistical measure that quantifies the deviation of a data point from the mean of a dataset in terms of standard deviations. It's a way to standardize data, making it easier to compare different datasets or observations.
To find the z-score, you use the formula:
z = (X - μ) / σ
Where X is the value in question, μ (mu) is the mean, and σ (sigma) is the standard deviation. Substituting the given values:
z = (59 - 66) / 3.5 = -7 / 3.5 = -2.00
Therefore, the z-score of a person who is 59 inches tall is -2.00, indicating they are 2 standard deviations below the average height.
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