Question

after examining a child at his 2 - year checkup, the boys pediatrician said that the z - score for his height relative to other 2 - year - olds in the country was - 1.25. explain to the parents what that means. he is 1.25 the mean in height for 2 - year - olds in the country.

Explanation:

Step1: Define z - score concept

The z - score is a measure of how many standard deviations an element is from the mean. The formula for the z - score is $z=\frac{x - \mu}{\sigma}$, where $x$ is the individual value, $\mu$ is the mean, and $\sigma$ is the standard deviation. In this case, $z=- 1.25$.

Step2: Interpret the negative z - score

A negative z - score means that the value of the boy's height ($x$) is below the mean height ($\mu$) for 2 - year - olds in the country. The magnitude of the z - score, 1.25, indicates that the boy's height is 1.25 standard deviations below the mean height of 2 - year - olds in the country.

Answer:

The boy's height is 1.25 standard deviations below the mean height for 2 - year - olds in the country.