a sample of n=25 scores has a mean of M=60 and a std dev of s=12. Find the z-score corresponding to each of the following scores from this sample.
X=66,X=48,X=84,X=55
for x=66 the z-score is (66-60)/12 = 0.5
do the rest the same way, the last one is (55-60)/12 = -0.417
To find the z-score corresponding to each of the given scores, we can use the formula:
Z = (X - M) / s
Where:
Z = z-score
X = the given score
M = mean
s = standard deviation
Let's calculate the z-score for each given score:
1. For X = 66:
Z = (66 - 60) / 12
Z = 6 / 12
Z = 0.5
The z-score corresponding to X = 66 is 0.5.
2. For X = 48:
Z = (48 - 60) / 12
Z = -12 / 12
Z = -1
The z-score corresponding to X = 48 is -1.
3. For X = 84:
Z = (84 - 60) / 12
Z = 24 / 12
Z = 2
The z-score corresponding to X = 84 is 2.
4. For X = 55:
Z = (55 - 60) / 12
Z = -5 / 12
Z ≈ -0.417
The z-score corresponding to X = 55 is approximately -0.417.