The national average for mathematics SATs in 2011 was 514 and the standard deviation was approximately 40. a) Within what boundaries would you expect at least 75% of the scores to fall?

If we solve for k we can do this:

So then we have at last 75% of the data withitn two deviations from the mean so the limits are:

Step-by-step explanation:

We don't know the distribution for the scores. But we know the following properties:

For this case we can use the Chebysev theorem who states that "At least of the values lies between and "

And we need the boundaries on which we expect at least 75% of the scores. If we use the Chebysev rule we have this:

If we solve for k we can do this:

So then we have at last 75% of the data withitn two deviations from the mean so the limits are:

a. is correct