Human adults in Europe have an average weight of 156lbs with a standard deviation of 22lbs. An elevator can hold 8 humans, but only if their average...

Human adults in Europe have an average weight of 156lbs with a standard deviation of 22lbs. An elevator can hold 8 humans, but only if their average weight is 175lbs or less. Use the Central Limit Theorem to calculate the following probabilities if a random selection of 8 humans walk into an elevator in Europe (show work):

a. Calculate the mean and standard deviation of the sample mean weight of 8 randomly selected humans.

b. Calculate the probability that a random selection of 8 humans will be too heavy to ride the elevator.