Given the mean of a data set is 254 and has a standard deviation of 12, which of the following data points would result in a z-score that indicates the data point is 2 standard deviations below the mean?(1 point) Responses 19.167 19.167 24 24 278 278 230

Answer 1

To find a data point that results in a z-score that indicates 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.

In this case, we want a z-score of -2 (indicating 2 standard deviations below the mean). The mean (\(\mu\)) is 254, and the standard deviation (\(\sigma\)) is 12.

We set up the equation:

\[ -2 = \frac{(X - 254)}{12} \]

Now, solving for \(X\):

1. Multiply both sides by 12: \[ -24 = X - 254 \]

2. Add 254 to both sides: \[ X = 254 - 24 \] \[ X = 230 \]

So, a data point of 230 will result in a z-score of -2, indicating it is 2 standard deviations below the mean.

Therefore, the answer is 230.