A university with a high water bill is interested in estimating the mean amount of time that students spend in the shower each day. In a sample of 32 students, the average time was 5.04 minutes and the samples standard deviation was 0.96 minutes. Using this sample information, construct a 99% confidence interval for the mean amount of time that students spend in the shower each day. (a) What is the lower limit of the 99% interval? Give your answer to three decimal places. (b) What is the upper limit of the 99% interval? Give your answer to three decimal places.