An apartment complex is designing a new elevator to carry 40

An apartment complex is designing a new elevator to carry 40 people. If the mean weight of humans is approximately 165 lbs with a standard deviation of 25 lbs, what should the elevator\'s maximum weight limit be so that it can carry the desired capacity 97% of the time? Round your answer up to the nearest pound. Why do you use the technique that you use?

Solution

If

X = k*x

and x has mean = u, standard deviation = s, then

X has mean = ku, and standard deviation = ks.

Thus, the mean of 40 people is

mean = 6600
standard deviation = 1000

Thus, first, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.97      
          
Then, using table or technology,          
          
z =    1.880793608      
          
As x = u + z * s / sqrt(n)          
          
where          
          
u = mean =    6600      
z = the critical z score =    1.880793608      
s = standard deviation =    1000      
n = sample size =    40      
Then          
          
x = critical value =    6897.379581 = 6898 lbs [ANSWER]