A criminologist has developed a questionnaire for predicting whether ateenager will become a delinquent. Scores on the questionnaire can range from 0 to 100, with higher values reflecting a presumably greater criminal tendency. As a rule of thumb, the criminologist decides to classify a teenager as a potential delinquent if his or her scoreexceeds 75. The questionnaire has already been tested on a large sample of teenagers, both delinquent and nondelinquent. Among those considered nondelinquent, scores were normally distributed with a mean of 60 and a standard deviation of 10. Among thoseconsidered delinquent, scores were normally distributed with a mean of 80 and a standard deviation of 5. In a randomly selected group of four considered delinquents, what is theprobability that the criminologist will classify all of them as delinquents? a. 0.8413b. 0.7531c. 0.5010d. 0.2469e. 0.1587

Question

Mathematics

Jayleen Pruitt

3 November, 13:20

A criminologist has developed a questionnaire for predicting whether ateenager will become a delinquent. Scores on the questionnaire can range from 0 to 100, with higher values reflecting a presumably greater criminal tendency. As a rule of thumb, the criminologist decides to classify a teenager as a potential delinquent if his or her scoreexceeds 75. The questionnaire has already been tested on a large sample of teenagers, both delinquent and nondelinquent. Among those considered nondelinquent, scores were normally distributed with a mean of 60 and a standard deviation of 10. Among thoseconsidered delinquent, scores were normally distributed with a mean of 80 and a standard deviation of 5. In a randomly selected group of four considered delinquents, what is theprobability that the criminologist will classify all of them as delinquents? a. 0.8413b. 0.7531c. 0.5010d. 0.2469e. 0.1587

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Answers (1)

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Rice · Answer 1

Probability=0.8413

So option A is correct.

Step-by-step explanation:

In order to find the probability that the criminologist will classify all of them as delinquents, we will proceed as following:

We are required to find:

P (m>=75|m-N (80,5))

it can be written as:

1-P (m<75|m-N (80,5))

P (m<75|m-N (80,5)) can be solved as

Z = (75-80) / 5

Z=-1

Probability = 1-Z (-1)

Fromm distribution table:

Probability=1-0.15866

Probability=0.8413

So option A is correct.