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 184 lb and a standard deviation of 23 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 to a 0.98 prpbability that this maximum will not be exceeded when 15 males are randomly selected. maximum weight - -lb Enter your answer rounded to the nearest whole number. Answers obtained using exact z-scores or Z-scores rounded to 3 decimal places are accepted. Question Help: Message instructor D Post to forum

Answer 1

one The men working for the Company have weights that normally distributed a meem of 18416 and standard deviation of 23 16. The the sum of neights of 15 randomly selected men is also normally distributed with meam 15X184 lb and Standard deviation 15 x 23 lb [ Since by Central limite the grem Sum of n nd with meam M and Standard deviation 6 is normaling distributed with mean nu and Standard deviation in weights of 15 ndomly selected men If y be the sum of rom Them - In 15x184 √15 x 23. ie 2= Y-2760 follows 89.079 Stand and normal distribution.

y* - 2760 = 2.054 89.079 y* - 2760 + 2.054 X 89.079 = 2942.97 o mum SPRCO The m anim to lokal allowable Weight = 2943 lb Maneir mum weight 2943 16