Question: A dispensing machine is set to produce 1-pound lots of a particular compound. The machine is fairly accurate, producing mean weights of 1 pound but standard deviation of 0.12 pounds. Thirty five lots are selected at random: a.) Probability that the sample mean weight is greater than 1 pound? b.) Probability that the sample mean weight is less than 0.95 pounds? c.) Probability that the sample mean weight is between 0.96 pounds and 1.04 pounds?