Suppose the average cholesterol level of children ages 2-14 is 175 mg/dL with a standard deviation = 30 mg/dL. Recently, doctors have started worrying about elevated cholesterol levels in some children. A study was done to see if there is a familial aggregation of cholesterol levels. Specifically, in families where the father had a heart attack and has elevated cholesterol levels (> 250 mg.dL), is the cholesterol level of the children in such families higher than 175? A group of 100 such children had an average cholesterol level of 207.3 mg/dL. Assume there were no outliers in the data set. Use a standard deviation = 30 mg/dL and find a 99% confidence interval for the average cholesterol level of all children whose father has had a heart attack with cholesterol level above 250. (Please give responses to 3 decimal places)