Question

What is the z-score of X, if n = 204, `mu= 15`, SD =1, and X =35?

Answer 1

`z=(X-mu)/(SD)=(35-15)/1=20` is the `z`-score of `X` itself. If you want the `z`-score of a mean `overline{X}=35`, the answer is `z=(overline{X}-mu)/((SD)/sqrt(n))=20/(1/sqrt(204)) approx 285.7`. Such high `z`-scores rarely occur in real life examples.