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 and (c) 140. Give a raw scores for persons whose Z scores on this test are (d) -1, (e) -0.8
and (f) 0.2.
(a) Z score = (100 - 150) / 25 = -2
(b) Z score = (120 - 150) / 25 = -1
(c) Z score = (140 - 150) / 25 = -0.4
(d) Raw score = -1 * 25 + 150 = 125
(e) Raw score = -0.8 * 25 + 150 = 130
(f) Raw score = 0.2 * 25 + 150 = 155
To calculate the z-scores, we can use the formula:
z = (x - mean) / standard deviation
Given that the mean is 150 and the standard deviation is 25, we can calculate the z-scores for the given scores:
a) z = (100 - 150) / 25
z = -2.00
b) z = (120 - 150) / 25
z = -1.20
c) z = (140 - 150) / 25
z = -0.40
To calculate the raw scores, we can rearrange the formula:
x = (z * standard deviation) + mean
Given the z-scores, we can calculate the raw scores:
d) x = (-1 * 25) + 150
x = 125
e) x = (-0.8 * 25) + 150
x = 130
f) x = (0.2 * 25) + 150
x = 155
So, the z-scores for the given scores are:
(a) -2.00
(b) -1.20
(c) -0.40
And the raw scores for the given z-scores are:
(d) 125
(e) 130
(f) 155
To calculate the z-scores, you can 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
Let's calculate the z-scores for the given data:
(a) To calculate the z-score for a raw score of 100:
z = (100 - 150) / 25
z = -2
(b) To calculate the z-score for a raw score of 120:
z = (120 - 150) / 25
z = -1.2
(c) To calculate the z-score for a raw score of 140:
z = (140 - 150) / 25
z = -0.4
Now let's find the raw scores for the given z-scores:
(d) To find the raw score for a z-score of -1:
-1 = (x - 150) / 25
-25 = x - 150
x = 125
(e) To find the raw score for a z-score of -0.8:
-0.8 = (x - 150) / 25
-20 = x - 150
x = 130
(f) To find the raw score for a z-score of 0.2:
0.2 = (x - 150) / 25
5 = x - 150
x = 155
Therefore, the answers are:
(a) z-score for 100: -2
(b) z-score for 120: -1.2
(c) z-score for 140: -0.4
(d) raw score for a z-score of -1: 125
(e) raw score for a z-score of -0.8: 130
(f) raw score for a z-score of 0.2: 155