# Recidivism. In the Scientific American article “Reducing Crime: Rehabilitation is Making a Comeback,” R. Doyle examined rehabilitation of felons. One aspect of the article discussed recidivism of juvenile prisoners between 14 and 17 years old, indicating that 82% of those released in 1994 were rearrested within 3 years. Suppose that, today, six newly releasedjuvenile prisoners between 14 and 17 years old are selected at random.a. Assuming that the recidivism rate is the same today as it was in 1994, determine the probability distribution for the number, Y , who are rearrested within 3 years.b. Determine and interpret the mean of Y .c. If, in fact, exactly two of the six newly released juvenile prisoners are rearrested within 3 years, would you be inclined to conclude that the recidivism rate today has decreased from the 82% rate in 1994? Explain your reasoning. Hint: First consider the probability P(Y ≤ 2).d. If, in fact, exactly four of the six newly released juvenile prisoners are rearrested within 3 years, would you be inclined to conclude that the recidivism rate today has decreased from the 82% rate in 1994? Explain your reasoning.

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Recidivism. In the Scientific American article “Reducing Crime: Rehabilitation is Making a Comeback,” R. Doyle examined rehabilitation of felons. One aspect of the article discussed recidivism of juvenile prisoners between 14 and 17 years old, indicating that 82% of those released in 1994 were rearrested within 3 years. Suppose that, today, six newly released
juvenile prisoners between 14 and 17 years old are selected at random.

a. Assuming that the recidivism rate is the same today as it was in 1994, determine the probability distribution for the number, Y , who are rearrested within 3 years.
b. Determine and interpret the mean of Y .
c. If, in fact, exactly two of the six newly released juvenile prisoners are rearrested within 3 years, would you be inclined to conclude that the recidivism rate today has decreased from the 82% rate in 1994? Explain your reasoning. Hint: First consider the probability P(Y ≤ 2).
d. If, in fact, exactly four of the six newly released juvenile prisoners are rearrested within 3 years, would you be inclined to conclude that the recidivism rate today has decreased from the 82% rate in 1994? Explain your reasoning.

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Step 1

a)

The random variable Y is the number of children who rearrested within 3 years. Here, 6 newly released juvenile prisoners between 14 and 17 years old is selected at random, that is. There is a 0.82 probability that the juvenile prisoners between 14 and 17 years old of those who released in 1994 were arrested within 3 years. Hence, the probability of success, .The two possible outcomes are the child is rearrested or the child is not rearrested (success or failure).Thus, Y follows binomial distribution.

The probability of obtaining Y successes in n independent trails of a binomial experiment is,

Step 2
Step 3

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