Question

After examining a child at his​ 2-year checkup, the​ boy's pediatrician said that the​ z-score for his height relative to other​ 2-year-olds in the country was 1.92 . Explain to the parents what that means.

Answer 1

Step-by-step explanation:z-score is a random variable that by definition follows a distribution whose mean is 0 and standard deviation is 1. (there many ways to get the score but it always behave like that).

So, given the above, a score of 1.92 means that the child's height is 1.92 standard deviations lower (because negative) than the average of the population.

If the heights of the population distribute according to the normal (Gaussian) distribution, the value 1.92 corresponds to about 20-th percentile of heights: about 20% if children in the population are of smaller height than this particular child.