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 184 lb and a standard deviation or 25 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 0.99 probability that this maximum will not be exceeded when 15 males are randomly selected. maximum weight = -lb Round to the nearest pound.

Answers obtained using exact z-scores or z-scores rounded to 2 decimal places are accepted.

I've been struggling on this problem for close to an hour... Can someone please help me out with the answer but also explain how its done so i can do it in the future?