Question

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.

Answer 1

Step 1

Given;

Step 2

State Chebychev's theorem

Thus;

`\begin{gathered} k=2 \\ 1-(1)/(2^2)=1-(1)/(4)=(3)/(4) \end{gathered}`

The empirical formula that applies to this is about 2 standard deviations of the mean

`\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}`

Answer;

`At\text{ least 75\% of the exam scores falls between 76 and 100}`