Piles are load tested to check their load carrying capacity. Suppose 8 piles are load tested for a building project. The capacity of each pile is 80, 85, 90, 75, 76, 84, 70, and 90 kip. Assume the sample standard deviation is equal to the population standard deviation. Assume the pile capacity can be modeled as a normal variable. The mean and standard deviation of pile capacity are 81.25 kip and 7.3 kip, respectively. (a) Calculate the 99% confidence interval for the mean. (b) Calculate the 99% lower confidence limit for the mean.