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 23 lb. You need to design an elevator that will safely carry 19 people. Assuming a worst case scenario of 19 male passengers, find the maximum total allowable weight if we want a 0.995 probability that this maximum will not be exceeded when 19 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

here expected mean weight of 19 male passenger =170*19 =3230

and standard deviation =23*(19)1/2 =100.2547

for 99.5 percentile ; z score =2.5758

therefore maximum allowable weight =mean +z*std deviation =3230 +2.5758*100.2547 =3488 Lb

(please try 3489 lb if above does not work due to rounding error)

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