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Incoming freshmen at a large high school routinely have their heights measured by the school nurse. The nurse records each height in inches and then determines the standardized $z$-score for each student.

How would the $z$-scores be affected if each height was converted from inches to centimeters? NOTE: $1 \text{ inch} = 2.54\text{ cm}$​


The $z$-scores will remain unchanged.


The $z$-scores will all be multiplied by $2.54$.


All $z$-scores will be increased by $1.54$.


All $z$-scores will be $254$% of their previous values.


There is no way to predict what will happen to the $z$-scores.

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