The capacity of an elevator is 8 people or 1384 pounds The c

The capacity of an elevator is 8 people or 1384 pounds The capacity will be exceeded if 8 people have weights with a mean greater than 1384/8 = 173 pounds. Suppose the people have weights that are normally distributed with a mean of 175 lb and a standard deviation of 33 lb. Find the probability that if a person is randomly selected, his weight will be greater than 173 pounds. Find the probability that 8 randomly selected people will have a mean that is greater than 173 pounds. Does the elevator appear to have the correct weight limit? Why or why not?

Solution

Maximum weight allowed per person = 173 pounds

X average weight of a person is N(175, 33)

a) P(X>173) =P(Z>-2/33) = 0.5239

b) For 8 people std error = 33/ rt 8 = 11.667

P(X bar>173) = P(Z>-0.171) = 0.5675

c) No. Option c is right.