Given the mean of a data set is 225 and has a standard deviation of 13, what is the value of the data point that would result in a z-score that indicates the data point is 2 standard deviations below the mean?
To find the value of the data point that is 2 standard deviations below the mean, we need to use the formula for calculating z-scores:
z = (X - μ) / σ
where:
z = z-score
X = the data point we want to find
μ = mean
σ = standard deviation
Given that the z-score is -2 (indicating 2 standard deviations below the mean), the formula becomes:
-2 = (X - 225) / 13
Solving for X:
-2 * 13 = X - 225
-26 = X - 225
X = -26 + 225
X = 199
Therefore, the value of the data point that is 2 standard deviations below the mean is 199.