48% of all violent felons in the prison system are repeat offenders. If 44 violent felons are randomly selected, find the following probabilities. Round answers to 4 places where possible. (a) Exactly 23 of them are repeat offenders. (b) At most 21 of them are repeat offenders. (c) At least 19 of them are repeat offenders. d) Between 16 and 20 (including 16 and 20) of them are repeat offenders.
48% of all violent felons in the prison system are repeat offenders. If 44 violent felons are randomly selected, find the following probabilities. Round answers to 4 places where possible. (a) Exactly 23 of them are repeat offenders. (b) At most 21 of them are repeat offenders. (c) At least 19 of them are repeat offenders. d) Between 16 and 20 (including 16 and 20) of them are repeat offenders.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 30PPS
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![**Statistical Probability in Criminal Recidivism**
In any given prison system, it is crucial to understand the patterns of repeat offences among violent felons for effective rehabilitation and policy formulation. Based on studies, 48% of all violent felons in the prison system are identified as repeat offenders. In a random selection of 44 violent felons, we can determine the probability of different scenarios regarding repeat offences. Below are some probabilistic assessments:
1. **Exactly 23 repeat offenders:**
Calculate the probability that exactly 23 out of the 44 felons are repeat offenders.
2. **At most 21 repeat offenders:**
Calculate the probability that 21 or fewer of the 44 felons are repeat offenders.
3. **At least 19 repeat offenders:**
Calculate the probability that 19 or more of the 44 felons are repeat offenders.
4. **Between 16 and 20 (inclusive) repeat offenders:**
Calculate the probability that the number of repeat offenders among the 44 felons falls between 16 and 20, both numbers included.
Please ensure that all answers are calculated and rounded to four decimal places where applicable to maintain accuracy and consistency in reporting.
Understanding these probabilities enlightens us on the dynamics of repeat offences, enabling more targeted interventions in the criminal justice system.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F82a8ebfc-76c9-419b-9ea9-29a90be836d5%2F035e3318-0fb8-49f0-931d-511bab4726f0%2Fi4yms9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Statistical Probability in Criminal Recidivism**
In any given prison system, it is crucial to understand the patterns of repeat offences among violent felons for effective rehabilitation and policy formulation. Based on studies, 48% of all violent felons in the prison system are identified as repeat offenders. In a random selection of 44 violent felons, we can determine the probability of different scenarios regarding repeat offences. Below are some probabilistic assessments:
1. **Exactly 23 repeat offenders:**
Calculate the probability that exactly 23 out of the 44 felons are repeat offenders.
2. **At most 21 repeat offenders:**
Calculate the probability that 21 or fewer of the 44 felons are repeat offenders.
3. **At least 19 repeat offenders:**
Calculate the probability that 19 or more of the 44 felons are repeat offenders.
4. **Between 16 and 20 (inclusive) repeat offenders:**
Calculate the probability that the number of repeat offenders among the 44 felons falls between 16 and 20, both numbers included.
Please ensure that all answers are calculated and rounded to four decimal places where applicable to maintain accuracy and consistency in reporting.
Understanding these probabilities enlightens us on the dynamics of repeat offences, enabling more targeted interventions in the criminal justice system.
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(D) Between 16 and 20 (including 16 and 20) of them are repeat offenders
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