# Question: In the Scientific American article Reducing Crime Rehabilitation is Making

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.

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.

## Relevant Questions

A success, s, in Bernoulli trials is often derived from a collection of outcomes. For example, an American roulette wheel consists of 38 numbers, of which 18 are red, 18 are black, and 2 are green. When the roulette wheel is ...Refer to the discussion on the binomial approximation to the hypergeometric distribution that begins on page 230. a. If sampling is with replacement, explain why the trials are independent and the success probability remains ...From Aneki.com, an independent, privately operated Web site based in Montreal, Canada, which is dedicated to promoting wider knowledge of the world's countries and regions, we obtained a frequency distribution of the number ...Use the frequentist interpretation of probability to interpret each of the following statements. a. The probability is 0.314 that the gestation period of a woman will exceed 9 months. b. The probability is 0.667 that the ...Construct a Venn diagram representing each event. a. (not E) b. (A or B) c. (A & B) d. (A & B & C) e. (A or B or C) f. ((not A) & B)Post your question