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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 182 lb and a standard deviation of 28 lb.
You need to design an elevator that will safely carry 20 people. Assuming a worst case scenario of 20 male passengers, find the maximum total allowable weight if we want a 0.98 probability that this maximum will not be exceeded when 20 males are randomly selected.
What is the maximum weight in lbs rounded to the nearest pound?
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