Math · Introductory statistics · Worked example
Find a percentile of a normal distribution
Heights are normal with mean 170 cm and standard deviation 8 cm. What height marks the 90th percentile?
Find the z for 0.90
Look for 0.90 inside the standard normal table: Φ(1.28) ≈ 0.8997 and Φ(1.29) ≈ 0.9015 bracket it, and more precisely z ≈ 1.2816.
Convert back
x = μ + zσ.
Result
About 180.3 cm: 90% of heights lie below it.
Your turn
Find the 25th percentile of the same heights.
Show the answer and explanation
About 164.6 cm.
Φ(−0.6745) ≈ 0.25, so x = 170 − 0.6745 × 8 ≈ 164.6.
Keep exploring
In Statistics, the standard normal table shows Φ(1.28) = 0.899727 and Φ(1.29) = 0.901475, bracketing 0.90.
Return to the concept →Sources and scope
Authored study material. Tool results depend on the stated inputs and model assumptions.
Try in the workspace
Open the example inputs, change a value and keep a useful result on your board.
Read the table in Statistics Open worked example on a board z-score in Math ReferenceYour existing work stays on this device. Examples open as editable copies.