An automatic machine in a manufacturing process is operating properly if the length of an important subcomponent is normally distributed with a mean µ =80 cm and a standard deviation σ =2 cm.
a. find the probability that the length of one randomly selected unit is less than 79 cm.
b. find the probability that the average length of 10 randomly selected units is less than 79 cm.
c. find the probability that the average length of 30 randomly selected units is less than 79 cm.