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 1.61. The pediatrician explains to the parents that the most extreme​ 5% of cases often require special treatment or attention. ​a) Does this child fall into that​ group? ​b) What do you need to assume about the heights of​ 2-year-olds to find your answer to part​ a?

Answer 1

No, the child doesn't fall into the extreme category. It is assumed that, heights of the children are in a normal distribution.

Explanation:

The 'critical value of z' for total 10% significance level, with 0.05 at each of the two sides, is = 1.645

Calculated z value 1.61 < critical point z value 1.645

So: the child falls within the 90% confidence interval & doesn't fall in the either of the two sided 5% extreme cases. Hence, the child doesn't need special treatment

The core assumption crucial to this z test conclusion is : The weight of children is in form of standard normal distribution. Then only, z results would be applicable.