The mean score on a Statistics exam is 88 points, with a standard deviation of 6 points. Apply Chebychev's Theorem to the data using k=2. Interpret the results.
![The mean score on a Statistics exam is 88 points with a standard deviation of 6 points Apply Chebychevs Theorem to the data using k2 Interpret the results class=](https://us-static.z-dn.net/files/dc4/a4cca1abf9ec941a20e0759453241cf5.png)
Step 1
Given;
Step 2
State Chebychev's theorem
Thus;
[tex]\begin{gathered} k=2 \\ 1-\frac{1}{2^2}=1-\frac{1}{4}=\frac{3}{4} \end{gathered}[/tex]The empirical formula that applies to this is about 2 standard deviations of the mean
[tex]\begin{gathered} (\mu+2\sigma)\text{ and \lparen}\mu-2\sigma) \\ (88+2(6))\text{ and \lparen88-2\lparen6\rparen\rparen} \\ 100\text{ and 76} \end{gathered}[/tex]Answer;
[tex]At\text{ least 75\% of the exam scores falls between 76 and 100}[/tex]