A program to reduce recidivism has been in effect for two years in a large northeastern state. A sociologist investigates the effectiveness of the program by taking a random sample of 200 prisons records repeat offenders. The records were selected from the files in the courthouse of the largest city in the state. The average length of time out of prison between the first and second offenses is 2.8 years with a standard deviation of 1.3 years. Calculate an 80% confidence interval for the mean prison-free time between first and second offenses (). Use the z-table since the z-table and t-table are very similar for a sample size of 200.