An ethanol railroad tariff is a fee charged for shipments of ethanol on public railroads. The Agricultural Marketing Service publishes tariff rates for railroad-car shipments of ethanol in the Biofuel Transportation Database. Assuming that the standard deviation of such tariff rates is $1150, determine the probability that the mean tariff rate of 500 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.