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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 183 lb and a standard deviation or 28 lb. You need to design an elevator that will safely carry 18 people. Assuming a worst case scenario of 18 male passengers, find the maximum total allowable weight if we want to a 0.995 probability that this maximum will not be exceeded when 18 males are randomly selected.
What is the maximum weight rounded to the nearest whole number?
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