The capacity of an elevator is 10 people or 1520 pounds. The capacity will be exceeded if 10 people have weights with a mean greater than 1520/10=152 pounds. Suppose the people have weights that are normally distributed with a mean of 162 lb and a standard deviation of 31 lb.
(a) Find the probability that if a person is randomly selected, his weight will be greater than 152 pounds. (round to four decimal places as needed)
(b) Find the probability that 10 randomly selected people will have a mean that is greater than 152 pounds. (Round to 4 decimal places as needed)