1. A certain homeowner's insurance company took a random sample of 190 claims that it paid in the year 2010. The average claim paid was $2125 with a standard deviation of o=$310. Find the error, a 95% confidence interval for u, and a brief explanation of the confidence interval. 2. At an archaeological site, ceramic clay vessels were discovered. 10 vessels were discovered with an average rim diameter of 15.8 centimeters and a sample standard deviation of s=3.5 centimeters. Find the error, an 80% confidence interval for the actual mean of the rim diameters of these clay vessels, and a brief explanation of your confidence interval. 3. An archer wants to be 99% confident of the proportion of her shots being in the center of the target (i.e., a bulls-eye). The archer takes 300 shots resulting in 60 bulls-eyes. Find the error, confidence interval for p, and a brief explanation of the confidence interval. 4. A random sample of bighorn sheep indicated the standard deviation of the sheep weights to be 15.8 pounds. How large of a sample size of bighorn sheep should be included in the sample to be 90% confident that the mean is within 2.5 pounds of all bighorn sheep