Answer
$474-554$, $2.5\%$
Work Step by Step
Empirical rule:
• Approximately 68% of the data values will fall within 1 standard deviation of the mean.
• Approximately 95% of the data values will fall within 2 standard deviations of the mean.
• Approximately 99.7% of the data values will fall within 3 standard deviations of the mean.
41. SAT Scores The national average for mathematics
SATs in 2011 was 514. Suppose that the distribution of
scores was approximately bell-shaped and that the standard
deviation was approximately 40. Within what
boundaries would you expect 68% of the scores to fall?
What percentage of scores would be above 594?
We can use the empirical rule for this bell-shaped distribution.
$68\%$ corresponds to within 1 standard deviation which means the boundaries are
$514-40$ to $514+40$ or $474-554$.
A score of 594 corresponds to $\frac{594-514}{40}=2$ standard deviations (SD), within 2SD
we have $95\%$ of the data and $1-0.95=0.05$ will be outside, so there will be half or $0.025$
above 594.
