Question

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.

Answer 1

Answer:

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

                                                                             $S.E = \frac{S.D}{\sqrt{n} }$

                                             Standard error = $\frac{1250}{\sqrt{350} } = 66.8153$

  by using normal distribution    $z = \frac{x -mean}{S.E}$

                                         $z = \frac{x^{-} -110}{66.8}$

                                   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