An automatic machine in a manufacturing process is operating properly if the lengths of an important subcomponent are normally distributed with a mean of 112 cm and a standard deviation of 5.3 cm.
A. Find the probability that one selected subcomponent is longer than 114 cm.
Probability =
B. Find the probability that if 3 subcomponents are randomly selected, their mean length exceeds 114 cm.
C. Find the probability that if 3 are randomly selected, all 3 have lengths that exceed 114 cm.
You can earn partial credit on this problem.