Criminologist: Job Description, Duties and Requirements

A criminologist developed a test to measure recidivism, where low scores indicate a lower probability of repeating the undesirable behavior. The test is formed so that it has a mean of 140 and a standard deviation of 40. 

The Percentile Rank of a Score of 172 

Mean = 140, Score = 172, Standard deviation = 40 

Z score = (X - μ) / σ 

Z = (172 – 140) /40 

Z = 0.8 

Conversion using the Z score chart gave 

0.7881 

Multiplied by 100 to gave the ranking 

0.7881 × 100 = 78.81% 

The answer is 78.81% 

The Z Score of a Test Score of 200 

Z score is calculated by getting the difference of the score from the mean divided by the standard deviation. In this case; 

Mean = 140, Score = 200, Standard deviation = 40 

Z = (X - μ) / σ 

Z = (200 – 140)/ 40 

Answer is Z score = 1.5 

Percentage of Scores That Falls Between 100 And 160 

Computation of the Z score of 100 

Z = (X - μ) / σ 

Z = (100 – 140) / 40 

Z = -1 

Conversion on Z score chart gave. 

0.1587 

Computation of the Z score of 160 

Z = (X - μ) / σ 

Z = (160-140) / 40 

Z = 0.5 

0.6915 

The area covered was obtained by, the difference of the value of 100 from the value of 160. 

0.6915 - 0.1587 

0.5328 

0.5328×100 = 53.28% 

Answer = 53.28% 

Proportion of Respondents That Should Score Above 190 

Computation of Z score for 190 

Z = (X - μ) / σ 

Z = (190-140) / 40 

Z = 1.25 conversion using the Z score chart gives 0.8944 

0.8944 representing proportion below 190 

To calculate for above 

(1- 0.8944) × 100 

The proportion that should score above 190 is 10.56% 

Recidivism Score For and Individual in the 67th Percentile in the Test 

The ranking divided by 100 to give; 67/100 = 0.67 

Using the Z score table, the corresponding Z score value is; 

Z = 0.44 

Using the formula Z = (X - μ) / σ 

Score = μ + (σ × Z) 

Score = 140 + (40×0.44) = 157.6 rounding off to 158 

The answer is 158.