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...

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 25 lb. You need to design an elevator that will safely carry 12 people. Assuming a worst case scenario of 12 male passengers, find the maximum total allowable weight if we want a 0.975 probability that this maximum will not be exceeded when 12 males are randomly selected.


maximum weight = -lb Round to the nearest pound.


Answers obtained using exactz-scores orz-scores rounded to 2 decimal places are accepted.