Answer :
Approximately 0.15% of the values lie below 2.
We need to determine how many standard deviations below the mean 2 is, and then use the 68-95-99.7 rule.
First, let's calculate how many standard deviations below the mean 2 is:
[tex]\[ \text{Number of standard deviations} = \frac{\text{value} - \mu}{\sigma} = \frac{2 - 14}{4} = \frac{-12}{4} = -3 \][/tex]
Since 2 is 3 standard deviations below the mean, we know from the 68-95-99.7 rule that:
- Approximately 99.7% of the data falls within three standard deviations below and above the mean.
- Therefore, approximately 0.15% of the data falls below three standard deviations below the mean.
So, approximately 0.15% of the values lie below 2.
