Given Problem -

A small time Albuquerque lawyer, Jimmy McGill, is trying to get his finances in order. He records his monthly income over an entire year to get an idea of how much money he can expect to make per month in order to see if he can afford his own private office. The following are his monthly incomes (in dollars) over an entire year: X1 = 6741 X2 = 6515 X3 = 7644 X4 = 8238 X5 = 6044 X6 = 5498 X7 = 9065 X8 = 7441 Xg = 4681 X10 = 6810 X11 = 6030 X12 = 6972 a.) Are the values normally distributed? Either draw or use R to create a QQ plot, a histogram, or a stem plot to check if the sample values appear normally distributed. What do you conclude? (Please include your R code and plot) (4pts.) b.) Assuming his monthly incomes are normally distributed, create an appropriate 95% and 99% confidence interval for Jimmy's true mean monthly income. Interpret these intervals. (6pts.)c.) If you know that the true standard deviation of Jimmy's monthly income is $1000, then create an appropriate 95% confidence interval for Jimmy's true mean monthly income. Interpret this interval. (4pts.) d.) Assuming o in part d.), what sample size is needed to ensure the margin of error is within + 500 dollars for a 99% large - sample confidence interval? (i.e. you'll need to use a z - critical value) (4pts.) e.) Do you think the confidence interval in part c.) will be accurate? Why or why not? (2pts.)