A distribution has a standard deviation of ó = 9.5. Find the z-score for a score above the mean by 4 points. note: round to 2 decimal places, and enter the value of the z-score but do not write "z = " in your answer
Z = (score-mean)/SD = 4/9.5 = ?
To find the z-score for a score above the mean by 4 points, we need to calculate the difference between the score and the mean, and then divide it by the standard deviation.
The formula to calculate the z-score is:
z = (x - μ) / σ
Where:
x = Score
μ = Mean
σ = Standard Deviation
In this case, the score is above the mean by 4 points, so we can set x = μ + 4.
Substituting the known values into the formula, we have:
z = (μ + 4 - μ) / σ
z = 4 / σ
Given that the standard deviation (σ) is 9.5, we can substitute it into the formula:
z = 4 / 9.5
Now we can calculate the z-score:
z = 0.42
Rounding to two decimal places, the z-score for a score above the mean by 4 points is 0.42.