Question

True or​ False: Chebyshev's inequality applies to all distributions regardless of​ shape, but the empirical rule holds only for distributions that are bell shaped.

Answer 1

True.

Explanation:

The empirical rule states that for a bell shaped distribution, nearly all of the data will fall within three standard deviations of the mean.

Chebyshev’s inequality says that at least
`1-(1)/(K^(2) )` of data from a sample will fall within
`K` standard deviations from the mean.

We have to remember that Chebyshev’s inequality has been proven mathematically for any distribution. But the empirical rule is a tool created for bell shaped distributions.