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 $1250, determine the probability that the mean tariff rate of 350 randomly selected railroad-car shipments of ethanol will be within $110 of the mean tariff rate of all railroad-car shipments of ethanol. Interpret your answer in terms of sampling error.

The probability that the mean is less than 110

P(x⁻<110) =0.5

Step-by-step explanation:

Explanation:-

Given the standard deviation of the Population' σ' = 1250

Given sample size 'n' = 350

The standard error of the mean determined by

                                             Standard error =

  by using normal distribution    

                                   cross multiplication  66.8z = x⁻-110

                                                                         x⁻  =  66.81Z+110

P(x⁻<110)=P(66.81Z+110<110)

             = P(66.81Z < 110-110)

            = P(66.81Z<0)

           = P(Z<0)

           = 0.5- A(z₁)

          = 0.5 - A(0)  (here z₁=0)

         = 0.5 -0.00

        =0.5

Conclusion:-                            

The probability that the mean is less than 110

P(x⁻<110) =0.5

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