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 179 lb and a standard deviation or 35 lb. You need to design an elevator that will safely carry 17 people. Assuming a worst case scenario of 17 male passengers, find the maximum total allowable weight if we want a 0.995 probability that this maximum will not be exceeded when 17 males are randomly selected.

maximum weight = -lb Round to the nearest pound.

Answers obtained using exact z-scores or z-scores rounded to 2 decimal places are accepted.

Explanation / Answer

z for 0.995 is 2.58

n = 17

mean = 179

SD = 35

(x - 179)/35/17 = 2.58

x = 200.9

Max weight = 200.9 * 17 = 3416

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