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?
A. 230
B. 24
C. 19.167
D. 278
A. 230
To calculate the z-score, use the formula:
z = (X - μ) / σ
Where:
X = data point
μ = mean (254)
σ = standard deviation (12)
z = (230 - 254) / 12
z = -24 / 12
z = -2
A z-score of -2 indicates that the data point is 2 standard deviations below the mean.
is this right
Apologies for the incorrect calculation. Let's try with the correct calculation:
The z-score formula is:
z = (X - μ) / σ
Given:
Mean (μ) = 254
Standard deviation (σ) = 12
Z-score = -2 (indicating 2 standard deviations below the mean)
Substitute the values into the formula and rearrange it to solve for X:
-2 = (X - 254) / 12
-24 = X - 254
X = -24 + 254
X = 230
Therefore, the correct data point that would result in a z-score indicating the data point is 2 standard deviations below the mean is 230.