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Women's weights are normally distributed with a mean of 143 lb and a standard deviation of 29 lb, and men's weights are normally distributed with a mean of 172 lb and a standard deviation of 29 lb (based on data from the National Health Survey). You need to design an elevator for the Westport Shopping Center, and it must safely carry 16 people. Assuming the worst case scenario of 16 male passengers, find the maximum total allowable weight if we want a 0.975 probability that this maximum will not be exceeded when 16 males are randomly selected.

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