In the year 2DXX, an investigative agency in the United States made the decision to implement statistical procedures to facilitate the capture of people for serious crimes. This agency collected motives, techniques and frequency of the crimes. data that were considered useful to establish a profile of criminals. The agency focused efforts on maintaining databases with criminal statistics, with the aim of predicting where and when an illegal act may occur. The results indicated that several cases had been solved thanks to the work of professional statisticians who, by providing estimates of residence rates for potential offenders and other I"lead" activities. assisted in making the arrests. All of this information turned out to be helpful in locating those on the most wanted lists. The statistically-based crime-fighting method included data on a wide variety of crimesl as well as the personal characteristics and habits of offenders. Data was kept on the number of crimes of each Iawbrealcer, the number of days that elapse between crimes, and the number of people who are killed by the police in the attempted arrest. Data is collected from a sample of 1,000 people who have committed a felony, revealing that. on average, criminals commit 12.4 illegal acts with a standard deviation of 4.? before they are arrested or killed. The data report that an average of 19.5 days elapse between criminal acts, with a standard deviation of 11.5 days. In addition, 212 of the 1.001] criminals who appear on the base lost their lives trying to elude the police. It is further assumed that a small sample is taken from a specific type of criminal. 15 observations of armed robbery reported the following amounts, in thousands of dollars: 45.5, 23.3, 45.3, 219, 54.3, 215, 33.4,12.6,?5.9,64.3, 54?, 115,214,534, and 34.9 Questions 1. Calculate and interpret the confidence intervals for the mean of illegal acts with 95% confidence. 2. Calculate and interpret the confidence intervals for the proportion of deaths when evading the police. with 95% confidence. 3. Calculate and interpret the confidence intervals for the mean armed robberies with 95% confidence. 4. Discuss the sample sizes, are they sufficient to achieve the objectives