A fitness company is building a 20-story high-rise. Architects building the high

Question

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 170 lb and a standard deviation or 30 lb. You need to design an elevator that will safely carry 15 people. Assuming a worst case scenario of 15 male passengers, find the maximum total allowable weight if we want a 0.975 probability that this maximum will not be exceeded when 15 males are randomly selected. maximum weight = -lb Round to the nearest pound.

Explanation / Answer

here for 15 male ; mean total weight =15*170=2550

and std deviation =30*(15)1/2 =116.1895

for 0.975 level ; critical value z =1.96

hence maximum weight =mean +z*std deviaiton =2550+1.96*116.1895=~ 2778 ( pounds)

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