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 ​$950, determine the probability that the mean tariff rate of 450 randomly selected railroad-car shipments of ethanol will be within ​$90 of the mean tariff rate of all railroad-car shipments of ethanol. Interpret your answer in terms of sampling error. A )The probability is ( ) ? enter your response here. ​(Round to three decimal places as​ needed.) B) 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 (?)  tariff rate of all railroad-car shipments of ethanol will be (?) ​$90. ​(Round to one decimal place as​ needed.)

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...