Correcting for a Finite Population The Boston Women's club needs an elevator lim- ited to 8 passengers. The club has 120 women members with weights that approxi- mate a normal distribution with a mean of 143 lb and a standard deviation of 29 lb. (Hint: See the discussion of the finite population correction factor.)
a. If 8 different members are randomly selected, find the probability that their total weight will not exceed the maximum capacity of 1300 lb.
b. If we want a 0.99 probability that the elevator will not be overloaded whenever 8 members are randomly selected as passengers, what should be the maximum allowable weight?