An ethanol railroad tariff is a fee charged for shipments of ethanol on public railroads. An agricultural association publishes tariff rates for? railroad-car shipments of ethanol. Assuming that the standard deviation of such tariff rates is ?$1100?, determine the probability that the mean tariff rate of 250 randomly selected? railroad-car shipments of ethanol will be within ?$100 of the mean tariff rate of all? railroad-car shipments of ethanol. Interpret your answer in terms of sampling error. The probability is __. (Round to three decimal places.)