Chebyshev’s inequality states that the probability that a random variable falls within k standard deviations of the mean of a probability distribution is at least

Checking this out in R for an arbitrary gamma distribution yields:

We can compare the two areas by first plotting the area under the gamma curve within k standard deviations of the mean:

and then superimposing the area specified by Chebyshev’s inequality:

Here we see that the area under the gamma curve within k standard deviations of the mean is greater than the limit specified by Chebyshev’s inequality.