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Maximum total allowable weight

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. You need to design an elevator for a shopping center and it must safely carry 16 people. Assuming a worst case scenario of 16 male passengers, find the maximum total allowable weight if we want a .975 probability that this maximum will not be exceeded when 16 males are randomly selected.

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## Q : Formula of t-quantile distribution

What is the formula of t-quantile distribution needed to calculate an exact 90% confidence interval for the difference between the population means?