A criminologist developed a test to measure recidivism, where low scores indicat

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.

a. What is the percentile rank of a score of 172?

b. What is the Z score for a test score of 200?

c. What percentage of scores falls between 100 and 160?

d. What proportion of respondents should score above 190?

e. Suppose an individual is in the 67th percentile in this test, what is his or her corresponding recidivism score?

Explanation / Answer

Mean = 140 and std dev = 40

Convert x score to z score

a) Percentile rank = 78.81% or 79th percentile

b) z score for 200 = 1.5

c) P(100<x<160) = 0.5328 = 53.28%

d) P(X>190) = 0.1056

e) 67th percentile z score = 0.74

x score = 140+0.74(40)

= 169.6

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