Converting from z-score

and back


Finding \(z\)-score:

\[z=\frac{x-\mu}{\sigma}\]

Finding normal value from \(z\)-score:

\[x=z\cdot\sigma+\mu\]

Finding data values for specific Probabilities:

Step 1

Draw a normal curve and shade the desired area that represents the probability, proportion, or percentile.

Step 2

Find the \(z\) value from the table that corresponds to the desired area.

Step 3

Calculate the \(x\) value by using the formula \(x=z\cdot\sigma+\mu\).