1. A criminologist developed a test to measure recidivism, where low scores indi

Question

1. 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 135 and a standard deviation of 40 (5pts). a) What is the percentile rank of a score of 170? b) What is the Z score for a test score of 180? c) What percentage of scores fall between 100 and 150? 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? 2. A small population of 10 cases has values of: 12, 5, 5, 6, 8, 9, 10, 2, 2, and 7. a) Calculate the mean and standard deviation for this population. Show all your work. (2pts).

Explanation / Answer

a) Z = (170-135)/40=0.875

P(Z<0.875) = 1-0.190787 = 0.809213

Percentile rank is 80.92%

b) Z = (180-135)/40=1.125

c) Z1 = (100-135)/40=-0.875

Z2 = (150-135)/40=0.375

P(-0.875<z<0.375) = 0.446 from z tables

d) Z = (190-135)/40 = 1.375

P(Z>1.375) =0.0846

8.46% respondents score above 190

e) Z for Cumulative Probability of 0.67 is 0.439913

Score = 135+40*0.439913= 152.59

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