An elevator near the office of one of the authors contains a sign that says its maximum capacity is 4,000 pounds or 26 people. It makes one wonder (well, at least it made one author wonder!), what is the probability that a random sample of 26 people would weigh over 4,000 pounds? 

a. The average weight of females in the United States (in 2010) was about 166 pounds with a standard deviation of about 60 pounds. What is the probability that 26 (randomly chosen) females get on the elevator and their combined weight exceeds 4,000 pounds? 

b. The average weight of males in the United States (in 2010) was about 196 pounds with a standard deviation of about 74 pounds. What is the probability that 26 (randomly chosen) males get on the elevator and their combined weight exceeds 4,000 pounds?