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 \(x=z\cdot\sigma+\mu\).