A fitness company is building a 20-story high-rise. Architects building the high-rise know that women working for the company have weights that are normally distributed with a mean of 143 lb and a standard deviation of 29 lb, and men working for the company have weights that are normally distributed with a mean of 178 lb and a standard deviation or 27 lb. You need to design an elevator that will safely carry 15 people. Assuming a worst case scenario of 15 male passengers, find the maximum total allowable weight if we want a 0.999 probability that this maximum will not be exceeded when 15 males are randomly selected. A maximum weight = -Ib Round to the nearest pound