On a measure of artistic ability the mean for college studen

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.

Solution

Z score of a value x of a series is defined as (x - mean(series))/SD(series) , where SD is Standard deviation

Here, we are considering series as scores for artistic ability of college students in New Zealand.

Mean=150, standard Deviatin=25.

Z scores for the following:

(a) 100: Z score=(100-150)/25 = -2

(b) 120: Z score=(120-150)/25 = -1.2

(c) 140: Z score=(140-150)/25 = -0.4

(d) 160: Z score=(160-150)/25 = 0.4

Raw score = Mean(series) +Z score * SD(series)

Raw scores for following:

(e) -1: Raw score= 150 +(-1)*25 = 125

(f) -0.8: Raw score= 150 +(-0.8)*25 = 130

(e) -0.2: Raw score= 150 +(-0.2)*25 = 145

(e) 1.38: Raw score= 150 +(1.38)*25 = 184.5