Statistics and probability in criminology

Supposed that, on average a random sample of 1000 daily newspapers edition contained 3.01 local crime stories per day, with a standard deviation of 2.65. Suppose that the distribution of crime stories in newspapers is normal. What is the Z score associated with a newspaper with 8 local crime stories? What proportion of newspapers published five or fewer crime stories? How many does this correspond to in the sample? What number of news stories corresponds to a Z score of +1? What percentages of newspapers publish between 1 and 6 local crime stories per day?

Suppose that a national survey of crime victimization have a sample of 144,400 researchers found that 16.2% of Americans age 12 or older had been a victim of crime. Estimate the percentage of US adults who were victims at the 95% confidence level. State in words the meaning of that result. Estimate the percentage of victims at the 99% confidence level. Now imagine that the Sample size was cut in half but the survey found the same value of 16.2% for the percentage of victims. By how much would the 95% confidence level and the 99% confidence interval increase?

Explain which of the following is a statistic and which is a parameter: The victimization rate for the population of US adults estimated by the government from the National Crime Victimization Survey. The mean salary of probation officers in the State Department of Correction. The percentage of tenth grade students who reported using heroin in the past month in the latest Watching the Future Survey. The mean age of Hispanic men from the 2010 decennial census.

Suppose that you are conducting a research on the commonness of severe binge drinking among college students. You define severe binge drinking as consuming 10 or more alcoholic beverages at a single sitting. You ask the question: "On how many days in the past two weeks have you consumed ten or more drinks at one time? The answers can range from 0 to 14. You collect data on a sample of 900 students. The average for this sample in 1.37 with a standard deviation of 0.80; Construct a 95% confidence interval for the average binge drinking score in the population.

Upon evaluation of the data another researcher agreed with your math and says it's correct, but question the normal distribution and says it isn't correct because the binge drinking scores are highly skewed, with some students binging very frequently, and the majority of students never binge drinking at all. Is the researcher correct that it is inappropriate to calculate a confidence interval for this research question?

What do statisticians mean by the terms empirical distribution and sampling distribution? Give 2 examples of each from a criminology or criminal justice perspective.