Question

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)
24
230
19.167
278

Explanation:

Step1: Recall the formula for z - score

The formula for z - score is \(z=\frac{x-\mu}{\sigma}\), where \(x\) is the data point, \(\mu\) is the mean, and \(\sigma\) is the standard deviation. We know that \(z=- 2\) (2 standard deviations below the mean), \(\mu = 254\), and \(\sigma=12\).

Step2: Solve for \(x\)

Substitute the values into the formula: \(-2=\frac{x - 254}{12}\).
Multiply both sides by 12: \(-2\times12=x - 254\).
\(-24=x - 254\).
Add 254 to both sides: \(x=254-24\).
\(x = 230\).

Answer:

230