a) A tax assessor collects 210 tax records and finds the mean tax for these records is $3,100. The standard deviation of the tax bills for all homeowners is $1,200.

a.1) What is the level of confidence and the significance level that the tax is between $2,800 and $3,400? Include calculation and solve with R.

a.2) Calculate the 90% confidence interval for the population mean based on the information provided in the question. Include calculation and solve with R.

a.3) What is the confidence interval within which we can be 100% confident that the interval contains the population mean? Include calculation and solve with R.

a.4) Include a graph showing the distribution of the population mean. Shade the curve to show $2,800 and $3,400, the corresponding level of confidence, shade the significance level, and label the sample mean and the sampling error tolerance E.