How this calculation works
Bound a one-sided tail probability using the variance and distance from the mean.
THE FORMULA
P(X−μ≥d) ≤ σ²/(σ²+d²)A worked example
With σ=3 and distance 4, the bound is 9/25.
Good to know
Requires finite variance. The result is an upper bound.
Reference: OpenStax Introductory Statistics (opens in a new tab) ↗
Read the result
Bound a one-sided tail probability using the variance and distance from the mean.
The primary result is labeled “Upper probability bound”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
Requires finite variance. The result is an upper bound.
For a related exercise, try the statistics calculator.
A few questions, answered
How can I check the default inputs by hand?
With σ=3 and distance 4, the bound is 9/25.
Which rule does this calculator apply?
P(X−μ≥d) ≤ σ²/(σ²+d²)