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.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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
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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