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

Trevor Rios

Mathematics

19 May, 13:07

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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Greta Morrow · 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.