Z-score Cut Off Calculator

This calculator determines the Z-score cut off value from the population mean, standard deviation, and percentile.

How to Use the Z-score Cut Off Calculator?

First, input the population mean (μ) and population standard deviation (σ) values.
Enter the x^th percentile value.
Now press the 'Calculate' button to generate results.
Finally, the calculator shows the Z-score cut off result with step-by-step calculation.

The Z-score cut off value can be calculated using the following steps:

First, find the Z-score value corresponding to the x^th percentile using the Z-score Table or Percentile to Z-score Calculator.

For example:

Now use the Z-score formula:

X = (Z × σ) + μ

Where,
X = Cutoff value,
Z = Z-score for the x^th percentile,
μ = Mean,
σ = Standard deviation.

Let's take an example.

Suppose, the mean is 82 and the standard deviation is 12. Calculate the Z-score cutoff value for the 99^th percentile.

Here,
Mean (μ) = 82,
Standard deviation (σ) = 12,
Percentile = 99^th.

1. Find the Z-score for the 99^th percentile.

Z = 2.32635

2. Put all the values in the formula.

X = (Z × σ) + μ

X = (2.32635 × 12) + 82

X = 27.9162 + 82

X = 109.916