Question

A criminologist developed a test to measure recidivism, where low scores indicated a lower probability of repeating the undesirable behavior. The test is normed so that it has a mean of 140 and a standard deviation of 40. Suppose an individual is in the 67th percentile in this exam.What is his or her corresponding recidivism score?

Answer 1

$\mu$ = 140

$\sigma$ = 40

67th percentile corresponds to area 0.67 - 0.50 =0.17 from mid value to RHS.

Table of Area Under Standard Normal Curve gives Z = 0.44

So,

Z = 0.44 = (X - 140)/40

So,

X = 140 + (0.44 X 40)

= 140 + 17.6 = 157.6

So,

Answer is:

157.6