1. A criminologist developed a test to measure recidivism (i. e., a person falling back into criminal behavior), in which low scores indicated a lower probability of repeating a criminal act. The test is normed so that it has a mean of 140 and a standard deviation of 40.

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

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Mathematics

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27 December, 01:43

1. A criminologist developed a test to measure recidivism (i. e., a person falling back into criminal behavior), in which low scores indicated a lower probability of repeating a criminal act. The test is normed so that it has a mean of 140 and a standard deviation of 40.

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

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Sofia Sharp · Answer 1

Let x be a random variable representin a person's recidivism score. Let the person's recidivism score be s, then:

P (x < s) = 0.67

P (z < (s - 140) / 40) = 0.67

Using normal distribution table,

P (z < 0.44) = 0.67

(s - 140) / 40 = 0.44

s - 140 = 40 x 0.44 = 17.6

s = 140 + 17.6 = 157.6

Therefore, the individual's corresponding recidivism score is 157.6