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 165 lb and a standard deviation or 32 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 probability that this maximum will not be exceeded when 15 males are randomly selected.

maximum weight =

Answer 1

Given that,

mean = = 165 lb

standard deviation = = 32 lb

n = 15

= = 165

= / n = 32 / 15 = 8.26

Using standard normal table

P(Z < z ) = 0.98

P(Z < 2.054 ) = 0.98

z = 2.054

Using z-score formula,

= z * +

= 2.054 * 8.26 + 165

= 181.97 lb.

maximum weight = 181.97 lb.