Trucks carry barrels of crude oil from a port in Texas to a distributer in New Mexico on long trailers. Filling equipment is used to fill the barrels with the oil. When functioning properly, the actual volume of oil loaded into each barrel by the filling equipment at the port is approximately normally distributed with a mean of 55 gallons and a standard deviation of 0.5 gallons. If the mean is greater than 55 gallons, the filling mechanism is overfilling.
If the filling equipment is functioning properly, what is the probability that the volume of oil in a randomly selected barrel will be 55.4 gallons or more? Show your work.
Suppose that the volume of oil in a randomly selected barrel is 55.4 gallons. Would that fact make you suspect that the filling mechanism is overfilling the barrels? Justify your answer.
If the filling equipment is functioning properly, what is the probability that a random
sample of 15 barrels have a mean volume of 55.4 gallons or more? Show your work.
Based on your answer in part (c), if a random sample of 15 barrels had a mean oil volume 55.4 gallons, would you suspect that the filling mechanism was overfilling the barrels? Justify your answer.