An automatic machine in a manufacturing process is operating properly if the lengths of an important subcomponent are normally distributed with mean = 117 cm and standard deviation = 5.2 cm. Find the...

An automatic machine in a manufacturing process is operating properly if the lengths of an important subcomponent are normally distributed with mean = 117 cm and standard deviation = 5.2 cm.

Find the probability that, if four subcomponents are randomly selected, their mean length exceeds 120 cm.

Find the probability that if four subcomponents are randomly selected, all four have lengths that exceed 120 cm.