Question 1099341
z (174)>(174-180)/26
>=-6/26=-0.231
=0.5913
For 12 people, the sd is 26/sqrt(12)=7.51
that z is >-6/7.51, or probability=0.7878
It is a higher probability that the weight limit will be exceeded, because the sample of 12 has a distribution whose mean is closer to the population mean of 180.  It is quite likely the elevator will be overloaded with 12 people.