A mining company needs to estimate the average amount of copper ore per ton mined. A random sample of 50 tons gives a sample mean of 146.75 pounds. The population standard deviation is assumed to be 35.2 pounds. We want to build a 95% confidence interval for the mean amount of copper per ton in the population of tons mined.

a. Check that the conditions to build a confidence interval are satisfied. State whether the critical value is from a Z-distribution or a T-distribution and why.

b. Find the margin of error for a 95% confidence interval. Round to the nearest tenth.