Suppose that IQ scores have a bell-shaped distribution with a mean of 99
and a standard deviation of 17
. Using the empirical rule, what percentage of IQ scores are between 82
and 116
?
Using the empirical rule, we know that:
- Approximately 68% of the data falls within 1 standard deviation of the mean
- Approximately 95% of the data falls within 2 standard deviations of the mean
- Approximately 99.7% of the data falls within 3 standard deviations of the mean
So, to find the percentage of IQ scores between 82 and 116, we can first calculate the z-scores for these values:
z-score for 82: (82 - 99) / 17 = -1
z-score for 116: (116 - 99) / 17 = 1
Now, we can calculate the percentage of IQ scores between these z-scores using the empirical rule:
Percentage = (68% + 95%) / 2 = 81.5%
Therefore, approximately 81.5% of IQ scores are between 82 and 116.