Apply Chebyshev's rule to answer the following question. A quantitative data set has mean 22 and standard deviation 3. At least what percentage of the observations lie between 16 and 28?

At least 75% of the observations lie between 16 and 28​.

Step-by-step explanation:

The Chebyshev’s Theorem says:

For any numerical data set, at least of the data lie within k standard deviations of the mean, that is, in the interval with endpoints for populations, where k is any positive whole number that is greater than 1.

Given:

The interval (16, 28) is the one that is formed by adding and subtracting two standard deviations from the mean.

For k = 2, we see that , which is 75% of the data must always be within two standard deviations of the mean.

At least 75% of the observations lie between 16 and 28​.

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