Complete question :
A clinical psychologist has developed a new measure for assessing alcohol abuse. In a normal (non-clinical) sample, he found that his measure had a mean equal to 85 and a standard deviation equal to 15. Identify the score 25th, 75th, 95th
Answer:
1.) 25th percentile = 74.95
2.) 75th percentile = 95.05
3.) 95th percentile = 109.75
Step-by-step explanation:
Given that :
Mean (m) = 85
Standard deviation (s) = 15
The Zscore, corresponding to the percentiles given:
25th percentile score corresponds to a Zscore of - 0.67
Recall the relation:
Zscore = (x - m) / sd
x = score; m = mean = 85 ; sd = standard deviation = 15
-0.67 = (x - 85) / 15
15 * - 0.67 = x - 85
-10.05 = x - 85
x = 74.95
2.) 75th percentile ; Zscore = 0.67
0.67 = (x - 85) / 15
15 * 0.67 = x - 85
10.05 = x - 85
x = 10.05 + 85
x = 95.05
3.) 95th percentile ; Zscore = 1.65
1.65 = (x - 85) / 15
15 * 1.65 = x - 85
24.75 = x - 85
x = 24.75 + 85
x = 109.75
