Answer:
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 [tex]1-\frac{1}{k^2}[/tex] of the data lie within k standard deviations of the mean, that is, in the interval with endpoints [tex]\mu \pm k\sigma[/tex] for populations, where k is any positive whole number that is greater than 1.
Given:
[tex]\mu=22\\\sigma=3[/tex]
The interval (16, 28) is the one that is formed by adding and subtracting two standard deviations from the mean.
[tex](\mu - k\sigma,\mu +k\sigma)\\(22 - 2\cdot3,22 + 2\cdot3)\\(16,28)[/tex]
For k = 2, we see that [tex]1-\frac{1}{2^2}=1-\frac{1}{4}=\frac{3}{4}[/tex], 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.
