How this calculation works
Invert the normal cumulative distribution to get a threshold at a chosen percentile.
THE FORMULA
Solve Φ(z)=p and return μ+σzA worked example
At the 50th percentile, the threshold equals the mean of 10.
Good to know
This assumes an already specified normal distribution.
Reference: OpenStax Introductory Statistics (opens in a new tab) ↗
Read the result
Invert the normal cumulative distribution to get a threshold at a chosen percentile.
The primary result is labeled “Quantile”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
This assumes an already specified normal distribution.
For a related exercise, try the statistics calculator.
A few questions, answered
How can I check the default inputs by hand?
At the 50th percentile, the threshold equals the mean of 10.
Which rule does this calculator apply?
Solve Φ(z)=p and return μ+σz