Each day a manufacturing plant receives a large shipment of drums of Chemical ZX-900. These drums are supposed to have a mean fill of 67 gallons and a standard deviation of fills of 0.4 gallons. Suppose that on a particular day the plant manager selects a random sample of 100 drums and finds that the mean fill of the 100 drums is 66.87 gallons. Assuming that the population standard deviation σ of all fills on the particular day is the 0.4 gallons that it is supposed to be, find the probability, if the population mean μ of all fills on the particular day is 67 gallons, of obtaining a sample mean fill that is less than or equal to 66.87 gallons. What do you conclude about whether μ is the 67 gallons it is supposed to be?