Final answer:
Approximately 97.5% of the data points are below 44 in a data set with a mean of 38 and a standard deviation of 3 using the empirical rule. This is because 44 is two standard deviations above the mean, and the empirical rule states about 95% of the data falls within two standard deviations of the mean.
Step-by-step explanation:
To determine the percent of data points that are below 44 in a data set with a mean of 38 and a standard deviation of 3 using the empirical rule, we will calculate how many standard deviations above the mean 44 is.
First, calculate the difference between 44 and the mean: 44 - 38 = 6. Then, divide this difference by the standard deviation: 6 / 3 = 2. This means 44 is two standard deviations above the mean.
According to the empirical rule:
- Approximately 68% of data falls within one standard deviation of the mean.
- About 95% falls within two standard deviations.
- Approximately 99.7% falls within three standard deviations.
Since 44 is two standard deviations above the mean, we can say that about 95% of the data falls below this value, as it encompasses the mean plus two standard deviations to either side. However, because we are only interested in the data below 44 (which is above the mean), we need to consider half of the 95% range, plus the 50% of data that falls below the mean.
The calculation will be 95% / 2 + 50% = 47.5% + 50% = 97.5%.
Thus, approximately 97.5% of the data points are below 44.