To find the data point that results in a z-score indicating that it is 2 standard deviations below the mean, we can use the formula for the z-score:
\[ z = \frac{(X - \mu)}{\sigma} \]
where:
- \( z \) is the z-score,
- \( X \) is the data point,
- \( \mu \) is the mean,
- \( \sigma \) is the standard deviation.
Given that:
- mean (\( \mu \)) = 254,
- standard deviation (\( \sigma \)) = 12,
- a z-score of -2 (which indicates 2 standard deviations below the mean).
We can set up the equation:
\[ -2 = \frac{(X - 254)}{12} \]
Now, solve for \( X \):
- Multiply both sides by 12:
\[ -24 = X - 254 \]
- Add 254 to both sides:
\[ X = 254 - 24 \]
\[ X = 230 \]
So, the data point 230 results in a z-score that is 2 standard deviations below the mean.
Therefore, the correct answer is 230.