for a population with mean of u=50 and a standard devation o=8,find the following raw scores corresponding to each of the following z scores.
z score 2.50,-.50,-1.50,.25,-1.00,.75
find the raw score(x) of the above numbers
Z = (score-mean)/SD
Insert values and calculate.
To find the raw score corresponding to a given z-score, you can use the formula:
x = z * o + u
Where:
x represents the raw score
z represents the z-score
o represents the standard deviation
u represents the mean
Let's calculate the raw score for each given z-score:
1. For z-score 2.50:
x = 2.50 * 8 + 50
x = 20 + 50
x = 70
So, the raw score corresponding to a z-score of 2.50 is 70.
2. For z-score -0.50:
x = -0.50 * 8 + 50
x = -4 + 50
x = 46
The raw score corresponding to a z-score of -0.50 is 46.
3. For z-score -1.50:
x = -1.50 * 8 + 50
x = -12 + 50
x = 38
The raw score corresponding to a z-score of -1.50 is 38.
4. For z-score 0.25:
x = 0.25 * 8 + 50
x = 2 + 50
x = 52
The raw score corresponding to a z-score of 0.25 is 52.
5. For z-score -1.00:
x = -1.00 * 8 + 50
x = -8 + 50
x = 42
The raw score corresponding to a z-score of -1.00 is 42.
6. For z-score 0.75:
x = 0.75 * 8 + 50
x = 6 + 50
x = 56
The raw score corresponding to a z-score of 0.75 is 56.
Therefore, the raw scores corresponding to the given z-scores are: 70, 46, 38, 52, 42, and 56.