An ethanol railroad tariff is a fee charged for shipments of ethanol on public railroads. An agricultural association publishes tariff rates forrailroad-car shipments of ethanol. Assuming that the standard deviation of such tariff rates is$1250,determine the probability that the mean tariff rate of500randomly selectedrailroad-car shipments of ethanol will be within$90of the mean tariff rate of allrailroad-car shipments of ethanol. Interpret your answer in terms of sampling error.

The probability is _____.

(Round to three decimal places asneeded.)

Interpret this probability in terms of the sampling error. Choose the correct answer below and fill in the answer box to complete your choice.

There is about a______%chance that the sampling error made in estimating the (variance of the/mean)tariff rate of allrailroad-car shipments of ethanol will be (at most/at least/exactly)$90.

(Round to one decimal place asneeded.)