Suppose the monthly cost of housing for a UNC student is a random variable with standard deviation equal to $130 dollars, however, we donEIt know the mean. a) We choose 70 UNC students at random and calculate the average monthly housing cost for the group to be $620. Find a 99% confidence interval for the population mean u. Give your endpoints to 2 decimal places. 99% condence interval for monthly cost of housing: ($ E . 35 E) b) What is the margin of error for this confidence interval? Give your answer to two decimal places. new: c) How large a sample of UNC students would we have to poll in order for our 99% margin of error to be less than $20? Your answer should be an integer