For a sample with a mean of M 45, a score of 59 corresponds to z 2.00. What is the sample standard deviation?
To find the sample standard deviation, we need to use the formula for calculating the z-score:
z = (x - M) / σ
We have the following information:
Mean, M = 45
Score, x = 59
z-score, z = 2.00
Plugging in the values into the formula, we can rearrange it to solve for the standard deviation:
2.00 = (59 - 45) / σ
Now, let's apply algebra to solve for σ:
2.00 = 14 / σ
Cross multiply:
2.00σ = 14
Divide both sides by 2.00:
σ = 14 / 2.00
σ = 7
Therefore, the sample standard deviation is 7.