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

The probability that the mean is less than 110

P(x⁻<110) =0.5

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 = (S.D)/(√(n) )`

Standard error =
`(1250)/(√(350) ) = 66.8153`

by using normal distribution
`z = (x -mean)/(S.E)`

`z = (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