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QuizMultiple Choice

Normal Distributions

Question 1 • SVH #CR Statistical Modeling 25-26

At age six, Kylie is 50 inches tall. Her height has a z-score of 1.8. At age four, Hannah is 48 inches tall. Her height has a z-score of 2.1. Relative to girls their ages, who is taller?

Answer
A
Kylie is taller because her z-score is lower than Hannah’s z-score.
B
Hannah is taller because her z-score is higher than Kylie’s z-score.
C
Kylie is taller because her z-score is closer to the mean than Hannah’s z-score.
D
Hannah is taller because her z-score is closer to the mean than Kylie’s z-score.

Explanation

To compare their heights relative to girls their own ages, compare their z-scores. A higher z-score means a height is farther above the age-group mean, so Hannah’s z-score of 2.1 indicates she is taller relative to girls her age than Kylie is relative to girls her age, with a z-score of 1.8. Therefore, the correct choice is B: Hannah is taller because her z-score is higher.

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