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

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

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