For a sample with a mean of M=45, a score of x=59 corresponds to z=2.00.What is the sample standard deviation?
Z = (score-mean)/SD
Insert the values and solve for SD.
To find the sample standard deviation, we need to use the z-score formula:
z = (x - M) / σ
Here, M represents the mean, x represents the score, σ represents the standard deviation, and z represents the z-score. In this case, we have the following information:
M = 45 (mean)
x = 59 (score)
z = 2.00
Substituting these values into the formula, we get:
2.00 = (59 - 45) / σ
To find the standard deviation, we need to rearrange the equation and solve for σ:
2.00σ = 59 - 45
2.00σ = 14
Dividing both sides of the equation by 2.00:
σ = 14 / 2.00
σ = 7
Therefore, the sample standard deviation is 7.