Suppose that a tax assessor wants to estimate the mean property tax bill for all homeowners living in College Park, Maryland. She collects 210 tax records and finds the mean tax for these records is $3,100. Suppose that we already know the standard deviation of the tax bills for all homeowners is $900.

2.1 What is the level of confidence and the significance level that the mean tax bill for all homeowners is between $2,700 and $3,500? Solve the questionby handANDwith R.

2.2 Use the 210 tax records, calculate the 85% confidence interval for the mean tax bills of all homeowners in College Park. Solve the questionby handANDwith R.

2.3 What is the confidence interval within which we can be 100% confident that the interval contains the mean tax of all homeowners in College Park? Solve the questionby handANDwith R.

2.4 Draw a graph showing the distribution of the sample mean (the sample has 210 tax records). Mark and label $2,700 and $3,500, shade and label the corresponding level of confidence, shade and label the significance level, and mark and label the sample mean and the sampling error toleranceE. Do this question by hand. You can draw a graph with tools (e.g., PowerPoint) or on paper then scan the graph into a picture (make sure the picture is clear and the handwriting is understandable).