The library elevator of a large university has a sign indicating a 16-person limit as well as a weight limit of 2500 lbs. When the elevator is full, we can think of the 16 people in the elevator as a random sample of people on campus. Suppose that the weight of students, faculty, and staff is normally distributed with a mean weight of 150 lbs and a standard deviation of 27 lbs. What is the probability that the total weight of a random sample of 16 people in the elevator will exceed the weight limit?