Question

What is the z-score of a value that is 0.52 standard deviations less than the mean?

Express your answer as a decimal.
my anwser was -0.62, Is it correct?

Answer 1

Is there a value associated for the mean and/or standard deviation ?

Answer 2

Actually I think you can resolve this without those numbers. The Z score is \[Z = \frac{X-\mu}{\sigma} \] and your given value, as stated in the problem, can be translated as \(X = \mu - 0.52 \sigma\), so: the Z score is \[ Z=\frac{(\mu - 0.52 \sigma)-\mu}{\sigma}=\frac{-0.52\sigma}{\sigma}=-0.52\]