An automatic machine in manufacturing procedure is operating properly if the lengths of significant sub component are normally distributed with mean =117 cm and standard deviation =5.2 cm.
a. Determine the probability that one chosen sub component is longer than 120 cm.
b. Determine the probability that if four subcomponents are randomly chosen, their mean length exceeds 120 cm.
c. Determine the probability that if four subcomponents are randomly chosen, all four have lengths that exceed 120 cm.