How this calculation works
The bound can be loose because the mean alone gives limited information about the distribution.
THE FORMULA
P(X ≥ t) ≤ min(1,E[X]/t)A worked example
A mean of 20 gives an upper bound of 0.4 at threshold 50.
Good to know
This is a bound and applies to nonnegative variables.
Reference: OpenStax Introductory Statistics (opens in a new tab) ↗
Read the result
Bound an upper-tail probability using the mean of a nonnegative random variable.
The primary result is labeled “Probability upper bound”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
This is a bound and applies to nonnegative variables.
For a related exercise, try the statistics calculator.
A few questions, answered
How can I check the default inputs by hand?
A mean of 20 gives an upper bound of 0.4 at threshold 50.
Which rule does this calculator apply?
P(X ≥ t) ≤ min(1,E[X]/t)