Acriminologist 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?

a). The percentile of a score of is .

b). The Z score for a test of 200 is .

c). The percentage of score between to is .

d). The proportion of respondents should score above is .

e). The corresponding score for percentile is .

Further Explanation:

The Z score of the standard normal distribution can be obtained as,

Given:

The mean of test is .

The standard deviation of the score is .

Explanation:

Part (a).

The Z score of can be obtained as,

The percentile of a score of can be obtained as,

From Z-table the percentile is .

Approximately .

Part (b).

The Z score for a test score can be obtained as,

The Z-score is .

Part (c).

The percentage of scores fall between and can be obtained as,

Further solve above equation.

Approximately the percentage is .

Part (d).

The proportion of respondent score above can be obtained as,

The proportion of respondents should score above is .

Part (e).

The Z-value of is .

The corresponding score for percentile can be obtained as,

The corresponding score for percentile is .

Learn more:

1. Learn more about normal distribution link

2. Learn more about standard normal distribution link

Answer details:

Grade: College

Subject: Statistics

Chapter: Normal distribution

Keywords: Z-score, standard normal distribution, standard deviation, criminologist, test, measure, probability, low score, mean, repeating, indicated, normal distribution, percentile, percentage, undesirable behavior, proportion.

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step-by-step explanation: