I'm going over some practice problems and I can't seem to figure this one out. Can anybody give me some help please?
On a measure of artistic ability, the mean for college students in New Zealand is 150 and the standard deviation is 25. Give the Z scores for New Zealand college students who score (a) 100, (b) 120, (c) 140, and (d) 160. Give the raw scores for persons whose Z scores on this test are (e) -1, (f) -.8, (g) -.2, and (h) +1.38.
Z = (score-mean)/SD
Fill in the values.
To find the Z scores for New Zealand college students, you need to use the formula:
Z = (X - μ) / σ
Where:
- Z is the Z score
- X is the raw score
- μ is the mean
- σ is the standard deviation
Now let's calculate the Z scores for each scenario:
(a) Z score for X = 100:
Z = (100 - 150) / 25
Z = -2
(b) Z score for X = 120:
Z = (120 - 150) / 25
Z = -1.2
(c) Z score for X = 140:
Z = (140 - 150) / 25
Z = -0.4
(d) Z score for X = 160:
Z = (160 - 150) / 25
Z = 0.4
Now let's find the raw scores for given Z scores using the formula:
X = μ + (Z * σ)
(e) Raw score for Z = -1:
X = 150 + (-1 * 25)
X = 125
(f) Raw score for Z = -0.8:
X = 150 + (-0.8 * 25)
X = 130
(g) Raw score for Z = -0.2:
X = 150 + (-0.2 * 25)
X = 145
(h) Raw score for Z = +1.38:
X = 150 + (1.38 * 25)
X = 183.5
So, the answers are:
(a) Z score for 100: -2
(b) Z score for 120: -1.2
(c) Z score for 140: -0.4
(d) Z score for 160: 0.4
(e) Raw score for Z = -1: 125
(f) Raw score for Z = -0.8: 130
(g) Raw score for Z = -0.2: 145
(h) Raw score for Z = +1.38: 183.5